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Complementarity Problems. Origins and Definitions

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Topological Methods in Complementarity Theory

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 41))

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Abstract

After more than thirty five years of research, the Complementarity Theory, with its applications in optimization, economics, engineering, mechanics, elasticity, game. theory, stochastic optimal control and sciences, has become a fruitful new domain in applied mathematics. It has also deep relations with fundamental mathematics.

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References

  • ALIZADEH, F. 1. Interior point methods in semidefinite programming with application to combinatorial optimization. Siam J. Opt. 5 (1995), 13–51.

    Article  MathSciNet  MATH  Google Scholar 

  • BARONTI, M. 1.The nonlinear complementarity problem and related questions. Rend. Mat. Appl. 6 (1986), 313–319.

    MathSciNet  MATH  Google Scholar 

  • BENSOUSSAN, A 1. Variational inequalities and optimal stopping time problems. In: Calculus of Variations and Control Theory (D. L. Russel (Ed.)), Academic Press (1976), 219–244.

    Google Scholar 

  • BENSOUSSAN, A, GOURSET, M. and LIONS, J. L. 1. Contrôle impulsionnel et inequations quasi-variationanelles stationnaires. C. R. Acad. Sci. Paris, 276 (1973), A 1279–1284.

    MATH  Google Scholar 

  • BENSOUSSAN, A and LIONS, J. L. 1. Problèmes de temps d’arrêt optimal et inéquations variationnelles parabo-liques. Applicable Anal. (1973), 267–294.

    Google Scholar 

  • BENSOUSSAN, A and LIONS, J. L. 2. Nouvelle formulation de problèmes de contrôle impulsionnel et applications. C. R. Acad. Sci. Paris, 276 (1973), A 1189–1192.

    MathSciNet  MATH  Google Scholar 

  • BENSOUSSAN, A and LIONS, J. L. 3. Nouvelles méthodes en contrôle impulsionnel. Appl. Math. Optim., 1 (1974), 289–312.

    Article  MathSciNet  Google Scholar 

  • BERSHCHANSKII, Y. M. and MEEROV, M. V. 1. The complementarity problem: Theory and methods of solutions. Automation and Remote Control 44 (1983), 687–710.

    Google Scholar 

  • BOD, P. 1. On closed sets having a least element. In: Optimization and Operations Research (W. Oettli and K. Ritter (Eds.)), Lecture Notes in Economics and Math. Systems, Springer-Verlag, 117 (1976), 23–34.

    Google Scholar 

  • BOD, P. 2. Sur un modèle non-linéaire des rapports interindustriels. Rairo, Recherche Oper. 11 Nr. 4 (1977), 405–415

    MathSciNet  MATH  Google Scholar 

  • BORWEIN, J. M. 1. Alternative theorems forgeneral complementarity problems. Preprint, Dalhousie University (1984).

    Google Scholar 

  • BORWEIN, J. M. 2. Generalized linear complementarity problems treated without fixed-point theory. J. Opt. Theory Appl, 43 Nr. 3, (1984), 343–356.

    Article  MATH  Google Scholar 

  • BORWEIN, J. M. and DEMPSTER, M. A. H. 1. The linear order complementarity problem. Math. Oper. Research 14 Nr. 3 (1989), 534–558.

    Article  MathSciNet  Google Scholar 

  • BULAVSKI, V., ISAC, G. and KALASHNIKOV, V. 1. Application of topological degree to complementarity problems. In: Multilevel Optimization: Algorithms and Applications (A. Migdalas, P. M. Pardalos, and P. Warbrant, P. (Eds)), Kluwer (1998), 333–358.

    Chapter  Google Scholar 

  • CAPUZZO-DOLCETTA, I. LORENZANI, M. and SPIZZICHINO, F. 1. Implicit complementarity problems and quasi-variational inequalities. In: Variational and Complementarity Problems. Theory and Applications. (R. W Cottle, F. Giannessi and J. L. Lions (eds.)), John Wiley & Sons (1980), 271–283.

    Google Scholar 

  • CAPUZZO-DOLCETTA, I. and MOSCO, U. 1. A degenerate complementarity system and applications to the optimal stoping Markov chains. Boll. Un. Imat. Ital. 95) 17-B, (1980), 692–703.

    Google Scholar 

  • CARBONE, A and ISAC, G. 1. The generalized order complementarity problem. Applications to economics. An existence result. In Nonlinear Studies 5 Nr. 2 (1998), 129–151.

    Google Scholar 

  • CHAN, D. and PANG, J. S. 1. The generalized quasivariational inequality problem. Math. Oper. Res. 7, Nr. 2 (1982), 211–222.

    Article  MathSciNet  MATH  Google Scholar 

  • CHEN GUANG-YA and YANG XIAO-Qi 1. The vector complementarity problem and its equivalence with the weak minimal element in ordered spaces. J. Math. Anal. Appl. 153 (1990), 136–158.

    Article  MathSciNet  Google Scholar 

  • COTTLE, R. W. 1. Nonlinear Programs with Positively Bounded Jacobians. Ph. D. Thesis, Department of Mathematics, University of California, Berkley (1964).

    Google Scholar 

  • COTTLE, R. W. 2. Note on a fundamental theorem in quadratic programming. Siam J. Appl. Math. , 12 (1964), 663–665.

    Article  MathSciNet  MATH  Google Scholar 

  • COTTLE, R. W. 3. Nonlinear programs with positively bounded Jacobians. Siam J. Appl Math. 14 Nr. 1 (1966), 147–158.

    Article  MathSciNet  MATH  Google Scholar 

  • COTTLE, R. W. 4. On a problem in linear inequalities. J. London Math. Soc. 43 (1968), 378–384.

    Article  MathSciNet  MATH  Google Scholar 

  • COTTLE, R. W. 5. Monotone solutions of the parametric linear complementarity problem. Math. Programming 3 (1972), 210–224.

    Article  MathSciNet  MATH  Google Scholar 

  • COTTLE, R. W. 6. Solution rays for a class of complementarity problems. Math. Programming Study 1 (1974), 59–70.

    Article  MathSciNet  Google Scholar 

  • COTTLE, R. W. 7. On Minkowski matrices in the linear complementarity problem. In: Optimization and Control, (R. Bulirsch, W. Oettli and J. Stoer (Eds.)), Lecture Notes in Mathematics, Springer-Verlag Nr. 477, (1975), 18–26.

    Google Scholar 

  • COTTLE, R. W. 8. Computational experience with large-scale linear complementarity problems. In: Fixed Points. (S. Karamardian (Ed.)), Academic Press (1976), 281–313.

    Google Scholar 

  • COTTLE, R. W. 9. Complementarity and variational problems. Symposia Mathematica 19 (1976), 177–208.

    MathSciNet  Google Scholar 

  • COTTLE, R. W. 10. Fundamentals of quadratic programming and linear complementarity. In: Engineering Plasticity by Math. Programming. (M. Z. Cohn and G. Maier (Eds.)), Pergamon Press (1979), 293–323.

    Google Scholar 

  • COTTLE, R. W. 11. Numerical methods for complementarity problems in engineering and applied science. In: Computing Methods in Applied Sciences and Engineering, 1977, I, (R, Glowinski and J. L. Lions (Eds.)), Lecture Notes in Mathematics, Springer-Verlag, Nr.704, (1979), 37–52.

    Google Scholar 

  • COTTLE, R. W. 12. Some recent developments in linear complementarity theory. In: Variational Inequalities and Complementarity Problems, (R. W. Cottle, F. Giannessi and J. L. Lions (Eds)), John Wiley & Sons, (1980), 97–104.

    Google Scholar 

  • COTTLE, R. W. 13. Completely-Q-matrices. Math. Programming 19 (1980), 347–351.

    Article  MathSciNet  MATH  Google Scholar 

  • COTTLE, R. W. 14. The principal pivoting method revisited. Math. Programming 48 (1990), 369–385.

    Article  MathSciNet  MATH  Google Scholar 

  • COTTLE, R. W. and DANTZIG, G. B. 1. A generalization of the linear complementarity problemm. J. Combinatorial Theory, 8 (1) (1970), 79–90.

    Article  MathSciNet  MATH  Google Scholar 

  • COTTLE, R. W., HABETLER, G.J. and LEMKE, C. E. 1. Quadratic forms semi-definite over convex cones. In: Proceedings of the Princeton Symposium on Mathematical Programming (H. W. Kuhn (Ed.)), Princeton University Press, Princeton, New Jersey (1970), 551–565.

    Google Scholar 

  • COTTLE, R. W., HABETLER, G.J. and LEMKE, C. E. 2. On classes of copositive matrices. Linear Algebra Appl. 3 (1970), 295–310.

    Article  MathSciNet  MATH  Google Scholar 

  • COTTLE, R. W., PANG, J. S. and STONE, R. E. 1. The Linear (omplementarity Problem. Academic Press, (1992).

    Google Scholar 

  • COTTLE, R. W. and VEINOTT, A. F. JR. 1. Polyhedral sets having a least element. Math. Programming 3 (1972), 238–249.

    Article  MathSciNet  MATH  Google Scholar 

  • DANTZIG, G. B. and COTTLE, R. W. 1. Positive semi-definite programming. In: Nonlinear Programming, (J. Abadie (Ed.)), North-Holland, Amsterdam (1967), 55 – 73 .

    Google Scholar 

  • DE MOOR, B. 1. Mathematical Concepts and Technics for Modelling of Static and Dynamic Systems. Ph D. Thesis, Dept., Electrical Engineering, Katholike Universiteit Leuven, Leuven, Belgium (1988).

    Google Scholar 

  • DE MOOR, B., VANDENBERGHE, L. and VANDENWALLE, J. 1. The generalized linear complementarity problem and an algorithm to find all its solutions. Math. Programming 57 (1992), 415–426.

    Article  MathSciNet  MATH  Google Scholar 

  • DE SHUTTER, B. and DE MOOR, B. 1. The extended linear complementarity problem. Math. Programming 71 (1995), 289–325.

    MathSciNet  Google Scholar 

  • DIRKSE, S. P. and FERRIS, M. C. 1. Mcplib: A collection of nonlinear mixed complementarity problem. Optim. Methods and Software 5 (1995), 319–345.

    Article  Google Scholar 

  • DORN, W. S. 1. Self dual quadratic programs. Siam J. Appl. Math. 9 Nr. 1 (1961), 51–54.

    Article  MathSciNet  MATH  Google Scholar 

  • DU VAL, P. 1. The unloading problem for plan curves. Amer. J. Math. 62 (1940), 307–311.

    Article  MathSciNet  MATH  Google Scholar 

  • EAVES, B. C. 1. The Linear Complementarity Problem in Mathematical Programming. Ph. D. Thesis, Department of Operations Research, Stanford University, Stanford, California (1969).

    Google Scholar 

  • EAVES, B. C. 2. On the basic theorem of complementarity. Math. Programming 1 (1971), 68–75.

    Article  MathSciNet  MATH  Google Scholar 

  • EAVES, B. C. 3. The linear complementarity problem. Management Sci. 17 Nr. 9 (1971), 612–634.

    Article  MathSciNet  MATH  Google Scholar 

  • EAVES, B. C. 4. Computing stationary points. Math. Programming Study 7(1978), 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  • EAVES, B. C. 5. Where solving for stationary points by Lcp is mixing Newton iterates. In: Homotopy Methods and Global Convergence, (B. C. Eaves, F. J. Gould, H. O. Peitgen and M. J. Todd (Eds.)), Plenum (1983), 63–78.

    Chapter  Google Scholar 

  • EAVES, B. C. 6. More with the Lemke complementarity algorithm. Math. Programming, 15 Nr. 2(1978), 214–219.

    MathSciNet  Google Scholar 

  • EAVES, B. C. 7. Thoughts on computing market equilibrium with Slcp. In: The Computation and Modelling of Economic Equilibrium, (A. Talman and G. Van der Laan, (Eds.)), Elsevier Publishing Co. Amsterdam, (1987), 1–18.

    Google Scholar 

  • EAVES, B. C. and LEMKE, C. E. 1. Equivalence of L.C.P. and P.L.C. Math. Oper. Research, 6 Nr. 4 (1981), 475–484.

    Article  MathSciNet  MATH  Google Scholar 

  • EAVES, B. C. 2. On the equivalence of the linear complementarity problem and system of piecewise linear equations. In: Homotopy Methods and Global Convergence, (B. C. Eaves, F. J. Gould, H. O. Peitgen and M. J. Todd (Eds.)), Plenum Press, (1983), 79–90.

    Chapter  Google Scholar 

  • EBIEFUNG, A. 1. The Generalized Linear Complementarity Problem and its Applications. Ph. D. Dissertation, Clemson University, Clemson , Sc 29634 (1991).

    Google Scholar 

  • EAVES, B. C. 2. Nonlinear mapping associated with the generalized linear complementarity. Math. Programming, 69 (1995), 255–268.

    MathSciNet  Google Scholar 

  • EAVES, B. C. 3. Existence theory and Q-matrix characterization for the generalized linear complementarity problem. Linear Alg. Appl. 223/224 (1995), 155–169.

    Article  MathSciNet  Google Scholar 

  • EBIEFUNG, A. and KOSTREVA, M. M. 1. The generalized Leontief input-output model and its application to the choice of new technology. Annals Oper. Res. 44 (1993), 161–172.

    Article  MathSciNet  MATH  Google Scholar 

  • FERRIS, M. C. and PANG, J. S. 1. Engineering and economic applications of complementarity problems. Siam Rev. 39 Nr. 4 (1997), 669–713.

    Article  MathSciNet  MATH  Google Scholar 

  • FUJIMOTO, T. 1. Nonlinear complementarity problems in function space. Siam J. Control Optim., 18 Nr. 6 (1980), 621–623.

    Article  MathSciNet  MATH  Google Scholar 

  • FUJIMOTO, T. 2. An extension of Tarski’s fixed point theorem and its applications to isotone complementarity problem. Math. Programming, 28 (1984), 116–118.

    Article  MathSciNet  MATH  Google Scholar 

  • FUJISAWA, T. and KUH, E. S. 1. Piecewise-linear theory of nonlinear network. Siam J. Appl. Math., 22 (1972), 307–328.

    Article  MathSciNet  MATH  Google Scholar 

  • FUJISAWA, T., KUH, E. S. and OHTSUKI, T. 1. A sparse matrix method for analysis of piecewise-linear resistive networks. Ieee Transactions on Circuit Theory 19 (1972), 571–584.

    Article  MathSciNet  Google Scholar 

  • GARCIA, C. A. 1. The Complementarity Problem and its Applications. Ph. D. Thesis, Rensselaer Polytechnic Institute, Troy, New York, (1973).

    Google Scholar 

  • GARCIA, C. A. 2. Some classes of matrices in linear complementarity theory. Math. Programming, 5 (1973), 299–310.

    Article  MathSciNet  MATH  Google Scholar 

  • GARCIA, C. A. 3. On the relationship on the lattice point problem, the complementarity problem and the set representation problem. Technical Report Nr. 145, Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, USA, (1973).

    Google Scholar 

  • GARCIA, C. A. 4. A note on a complementarity variant of Lemke’s methods. Math. Programming 10 (1976), 134–136.

    Article  MathSciNet  MATH  Google Scholar 

  • GARCIA, C. A. 5. A note on a complementarity problem. J.Opt. Theory Appl. 21 Nr. 4 (1977), 529–530.

    Article  MATH  Google Scholar 

  • GARCIA, C. B., GOULD, F. J. and TURNBULL, T. R. 1. A PL homotopy method for the linear complementarity problem. In: Mathematical Programming, (R. W. Cottle, M. L. Kelmanson and B. Korte (Eds.)), North-Holland, Amsterdam, (1981), 113–145.

    Google Scholar 

  • GARCIA, C. B., GOULD, F. J. and TURNBULL, T. R. 2. Relation between PL maps, complementarity cones and degree in linear complementarity problems. In: Homotopy Methods and Global Convergence, (B. C. Eaves, F. J. Gould, H. O. Peitgen and M.J. Todd (Eds)), Plenum Press, New York, (1983), 91–144.

    Chapter  Google Scholar 

  • GARCIA, C. B. and LEMKE, C. E. 1. All solutions to linear complementarity problems by implicit search. R. P. I. Math. Rep. Nr. 91, Rensselaer Polytechnic Institute, Troy, New York, (1970).

    Google Scholar 

  • GOULD, F. J. and TOLLE, J. W. 1. A unified approach to complementarity in optimization. Discrete Mathematics, 7 (1974), 225–271.

    Article  MathSciNet  MATH  Google Scholar 

  • GOULD, F. J. and TOLLE, J. W. 2. Complementarity Pivoting on a Pseudomanifold with Applications in the Decision Sciences. Heldermann Verlag, Berlin (1983).

    Google Scholar 

  • GOWDA, M. S. 1. Pseudomonotone and copositive-star matrices. Linear Algebra and its Applications, 113 (1989), 107–110.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. 2. Complementarity problems over locally compact cones. Siam J. Control Opt., 27 (1989), 836–841.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. 3. Affine pseudomonotone mappings and the linear complementarity problem. Siam J. Matrix Anal. Appl. 11 (1990), 373–380.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. 4. On Q-matrices. Math. Programming 49, (1990), 139–142.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. 5. On the transpose of a pseudomonotone matrix and the Lcp. Linear Algebra Appl. 140 (1990), 129–137.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. 6. Applications of degree theory to linear complementarity problems. Math. Oper. Res. 18 (1993), 868–879.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. 7. On reducing a monotone horizontal Lcp to an Lcp. Appl. Math. Letters 8(1994) 97–100

    Article  MathSciNet  Google Scholar 

  • GOWDA, M. S. 8. On the extended linear complementarity problem. Math. Programming 72 (1996), 33–50.

    MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. 9. An analysis of zero set and global error bound properties of a piecewise affine function via its recession function. Siam J. Matrix Anal. Appl. 17 Nr. 3 (1996), 594–609.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. and PANG, J. S. 1. On solution stability of the linear complementarity problem. Math. Oper. Research 17 (1992), 77–83.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. and PANG, J. S. 2. The basic theorem of complementarity revisited. Math. Programming 58 (1993), 161–177.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. and PANG, J.S. 3. On the boundedness and stability of solutions to the affine variational inequality problem. Siam J. Control and Opt. 32 (1994), 421–441.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. and PANG, J. S. 4. Stability analysis of variational inequalities and nonlinear complementarity problems, via the mixed linear complementarity problem and degree theory. Math. Oper. Research, 19 (1994), 831–879.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. and SEIDMAN, T. I. 1. Generalized linear complementarity problems. Math. Programming 46 (1990), 329–340.

    Article  MathSciNet  MATH  Google Scholar 

  • GOWDA, M. S. and SZNAJDER, R. 1. The generalized order linear complementarity problem. Siam J. Matrix Anal. Appl. 15 Nr. 3 (1994), 779–795.

    Article  MathSciNet  MATH  Google Scholar 

  • HABETLER, G. J. and KOSTREVA, M. M. 1. On a direct algorithm for nonlinear complementarity problem. Siam J. Control Opt., 16 Nr. 3 (1978), 504–511.

    Article  MathSciNet  MATH  Google Scholar 

  • HABETLER, G. J. and KOSTREVA, M. M. 2. Sets of generalized complementarity problems and P-matrices. Math. Oper. Res., 5 Nr. 2 (1980), 280–284.

    Article  MathSciNet  MATH  Google Scholar 

  • HARKER, P. T. and PANG, J. S. 1. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Math. Programming, Series B, Nr. 48 (1990), 161–220.

    Article  MathSciNet  MATH  Google Scholar 

  • HARRISON, J. M and REIMAN, M. I. 1. Reflected Brownian motion on an orthant. Annals of Probability, 9 (1981), 302–308.

    Article  MathSciNet  MATH  Google Scholar 

  • HARRISON, J. M. and SHEPP, L. A. 1. A tandem storage system and its diffusion limit. Stoch. Proc. and Appl. 16 (1984), 257–274.

    Article  MathSciNet  MATH  Google Scholar 

  • HIPFEL, D. M. 1. The Nonlinear Differential Complementarity Problem. Ph. Thesis, Rensselaer Polytechnic Institute Troy, New York, (1993).

    Google Scholar 

  • INGLETON, A. W. 1. A problem in linear inequalities. Proc. London Math. Soc. 16 (1966), 519–536.

    Article  MathSciNet  MATH  Google Scholar 

  • INGLETON, A. W. 2. The linear complementarity problem. J. London Math. Soc;. (2) 2 (1970), 330–336.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. 1. Un théorème de point fixe. Application au problème d’optimisation d’Ersov. Sem. Inst. Math. Appl. Giovanni Sansone, Univ. Firenze, Rept. (1980).

    Google Scholar 

  • ISAC, G. 2. Complementarity problem and coincidence equations on convex cones. In: Methods of Operations Research (K. Ritter, W. Oettli and R. Henn (Eds.)), Verlagsgruppe Athenäum, Hain, Hanstein, 51 (1984), 23–33.

    Google Scholar 

  • ISAC, G. 3. Nonlinear complementarity problem and Galerkin method. J. Math. Anal. Appl. 108 Nr. 2 (1985), 5663–574

    Article  MathSciNet  Google Scholar 

  • ISAC, G. 4. On implicit complementarity problem in Hilbert spaces. Bull. Austr. Math. Soc. 32 Nr. 2 (1985), 251–260.

    Article  MathSciNet  Google Scholar 

  • ISAC, G. 5. Complementarity problem and coincidence equations on convex cones. Boll. Un. Mat. Ital. (6), 5–1B (1986)925–943.

    Google Scholar 

  • ISAC, G. 6. Problèmes de complémentarité. (En dimension infinie). Mini-cours. Publica-tions du Dép. de Math. et Informatique Univ. de Limoges (France) (1985).

    Google Scholar 

  • ISAC, G. 7. Fixed point theory and complementarity problems in Hilbert spaces. Bull. Austr. Math. Soc. 36 Nr. 2 (1987), 295–310.

    Article  MathSciNet  Google Scholar 

  • ISAC, G. 8. Fixed point theory, coincidence equations on convex cones and complemen-tarity problem. Contemporary Math. 72, (1988). 139–155.

    Article  MathSciNet  Google Scholar 

  • ISAC, G. 9. On some generalization of Karamardian’s theorem on the complementarity problem. Boll. U.M.I. (7) 2-B (1988), 323–332.

    Google Scholar 

  • ISAC, G. 10. The numerical range theory and boundedness of solutions of the complementarity problem. J Math. Anal. Appi. 143 Nr. 1 (1989), 235–251.

    Article  MathSciNet  Google Scholar 

  • ISAC, G. 11. A special variational inequality and the implicit complementarity problem. J. Fac. Sci. Univ. Tokyo Sect. Ia, Math. 37 (1990), 109–127.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G. 12. Iterative methods for the general order complementarity problem. In: Approximation Theory, Spline Functions and Applications, (S. P. Singh (Ed.)), Kluwer Academic Publisher (1992), 365–380.

    Chapter  Google Scholar 

  • ISAC, G. 13. Complementarity Problems. Lecture Notes in Mathematics Nr. 1528, Springer-Verlag (1992).

    MATH  Google Scholar 

  • ISAC, G. 14. Fixed point theorems on convex cones, generalized pseudo-contractive mappings and the complementarity problem. Bull. Institute Math. Academia Sinica 23 Nr. 1 (1995), 21–35.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G. 15. The fold complementarity problem and the order complementarity problem. Topological Meth. Nonlinear Anal. 8 (1996), 343–358.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G. 16. Exceptional families of elements for k-set fields in Hilbert spaces and complementarity theory. In: Proceed. International Conf. Opt. Tech. Appl. Icota’98, Perth Australia, 1135–1143.

    Google Scholar 

  • ISAC, G., BULAVSKI, V. and KALASHNIKOV, V. 1. Exceptional families, topological degree and complementarity problems. J. Global Opt. 10 (1997), 207–225.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and CARBONE, A. 1. Exceptional families of elements for continuous functions. Some applications to complementarity theory. Forthcoming: J. Global Opt.

    Google Scholar 

  • ISAC, G. and GOELEVEN, D. 1. Existence theorem for the implicit complementarity problem. International J. Math. and Math. Sci. 16 Nr. 1 (1993), 67–74.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and GOELEVEN, D. 2. The implicit general order complementarity problem, models and iterative methods. Annals of Oper. Res. 44 (1993), 63–92.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and GOWDA, M. S. 1. Operators of class (S) 1 +, Altman’s condition and the complementarity problem. J. Fac. Sci. Univ. Tokio Sect. Ia Math. 40 (1993), 1–16.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G. and KOSTREVA, M. M. 1. The generalized order complementarity problem. J. Opt. Theory Appl. 71 Nr. 3 (1991), 517–534.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and KOSTREVA, M. M. 2. Kneser’s theorem and multivalued generalized order complementarity problem. Appl. Math. Lett. 4 Nr. 6 (1991), 81–85.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and KOSTREVA, M. M. 3. The implicit generalized order complementarity problem and Leontief’s input -output model. Applicationes Mathematicae 24 Nr. 2 (1996), 113–125.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G., KOSTREVA, M. M. and POLYASHUK, M. 1. Relational complementarity problem. Preprint (1998)

    Google Scholar 

  • ISAC, G., KOSTREVA, M. M. and WIECEK, M. M. 1. Multiple-objective approximation offeasible but unsolvable linear comple-mentarity problem. J. Opt. Theory Appl., 86 Nr. 2 (1995), 389–404.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and OBUCHOWSKA, W. T. 1. Functions without exceptional family of elements and complementarity problems. To appear in: J. Opt. Theory Appl. 99, Nr. 1(1998). 147–163.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and ThéRA, M. 1. A variational principle. Application to the nonlinear comnplementarity problem. In: Nonlinear and Convex Analysis (Proceedings in honor of Ky Fan). (B. L. Lin and S. Simons (Eds.)), Marcel Dekker (1987), 127–145.

    Google Scholar 

  • ISAC, G. and ThéRA, M. 2. Complementarity problem and the existence ofthe post-critical equilibrium state of a thin elastic plate. J. Optim. Theory Appl. 58 Nr. 2 (1988), 241–257.

    Article  MathSciNet  MATH  Google Scholar 

  • KANEKO, I. 1. The nonlinear complementarity problem. Term Paper, Or 340 C, Department of Operations Research, Stanford University, Stanford, Ca. (1973).

    Google Scholar 

  • KANEKO, I. 2. Parametric Complementarity Problem. Ph. D. Thesis, Stanford University, Stanford, California, (1975).

    Google Scholar 

  • KANEKO, I. 3. Isotone solutions of parametric linear complementarity problems. Math. Programming 12 (1977), 48–59.

    Article  MathSciNet  MATH  Google Scholar 

  • KANEKO, I. 4. A parametric linear complementarity problem involving derivatives. Math. Programming 15 (1978), 146–154.

    Article  MathSciNet  MATH  Google Scholar 

  • KANEKO, I. 5. A linear complementarity problem with an n by 2n P-matrices. Math. Programming Study 7 (1978), 120–141.

    Article  MATH  Google Scholar 

  • KANEKO, I. 6.A maximization problem related to parametric linear complementarity. Siam Journal Control Opt. 16, Nr. 1 (1978), 41–55.

    Article  MATH  Google Scholar 

  • KANEKO, I. 7. A maximization problem related to linear complementarity. Math. Programming 15 Nr.2 (1978), 146–154.

    Article  MathSciNet  MATH  Google Scholar 

  • KANEKO, I. 8. Linear Complementarity problems and characterizations of Minkowski matrices. Linear Algebra and its Appl., 20 (1978), 113–130.

    Article  Google Scholar 

  • KANEKO, I. 9. The number of solutions of a class of linear complementarity problems. Math. Programming, 17 (1979), 104–105.

    Article  MathSciNet  MATH  Google Scholar 

  • KANEKO, I. 10. A reduction theorem for the linear complementarity problem with a certain patterned matrix. Linear Algebra and its Appl. 21 (1978), 13–34.

    Article  MATH  Google Scholar 

  • KANEKO, I. 11. O some recent engineering applications of complementarity problems. Math. Programming Study, 17 (1982), 111–125.

    Article  MATH  Google Scholar 

  • KANEKO, I. 12. Complete solutions for a class of elastic-plastic structures. Comput. Methods Appl. Mech Engineering, 21 (1980), 193–209.

    MATH  Google Scholar 

  • KANEKO, I. 13. Piecewise linear elastic-plastic analysis. International J. Num. Methods in Engineering 14 (1979), 757–767.

    Article  MATH  Google Scholar 

  • KARAMARDIAN, S. 1. The nonlinear complementarity problem with applications. Part 1. J. Opt. Theory Appl. 4 (1969), 87–98.

    Article  MathSciNet  MATH  Google Scholar 

  • KARAMARDIAN, S. 2. The nonlinear complementarity problem with applications. Part 2. J. Opt. Theory Appl. 4 (1969), 167–181

    Article  MathSciNet  MATH  Google Scholar 

  • KARAMARDIAN, S. 3. Generalized complementarity problem. J. Opt. Theory Appl. 8(1971), 161–168.

    Article  MathSciNet  MATH  Google Scholar 

  • KARAMARDIAN, S. 4. The complementaritv problem. Math. Programming 2 (1972), 107–129.

    Article  MathSciNet  MATH  Google Scholar 

  • KARAMARDIAN, S. 5. Complementarity problems over cones with monotone and pseudo-monotone maps. J. Opt. Theory Appl. 18 (1976), 445–454.

    Article  MathSciNet  MATH  Google Scholar 

  • KARAMARDIAN, S. 6. An existence theorem for the comnplementarity problem. J. Opt. Theory Appl. 19 (1976), 227–232.

    Article  MathSciNet  MATH  Google Scholar 

  • KOJIMA, M. 1. Computational methods for solving nonlinear complementarity problems. Keio Engineering Report 27 (1974), 1–41.

    MathSciNet  Google Scholar 

  • KOJIMA, M. 2. A unification of the existence theorems of the nonlinear complementarity problem. Math. Programming 9 (1975), 257–277.

    Article  MathSciNet  MATH  Google Scholar 

  • KOJIMA, M. 3. Studies on piecewise-linear approximations of piecewise-C1 mappings in fixed points and complementarity theory. Math. Oper. Research 3 (1978), 17–36.

    Article  MathSciNet  MATH  Google Scholar 

  • KOJIMA, M. 4. A complementarity pivoting approach to parametric nonlinear programming. Math. Oper. Res. 4 Nr. 4 (1979), 464–477.

    Article  MathSciNet  MATH  Google Scholar 

  • KOJIMA, M., MIZUNO, S. and NOMA, T. 1. A new continuation method for complementarity problems with uniform P-functions. Math. Programming 43 (1989), 107–113.

    Article  MathSciNet  MATH  Google Scholar 

  • KOJIMA, M., MIZUNO, S. and NOMA, T. 2. Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems. Math. Oper. Research 15 (1990), 662–675.

    Article  MathSciNet  MATH  Google Scholar 

  • KOJIMA, M., NISHINO, H. and SEKINE, T. 1. An extension of Lemke’s method to the piecewise linear complementarity method. Siam J. Appl. Math., 31 (1976), 600–613.

    MathSciNet  MATH  Google Scholar 

  • KOJIMA, M. and SAIGAL, R. 1. On the number of solutions to a class of linear complementarity problems. Math. Programming, 17 (1979), 136–139.

    Article  MathSciNet  MATH  Google Scholar 

  • KOJIMA, M. and SAIGAL, R. 2. On the number ofsolutions to a class of complementarity problems. Math. Programming, 21 (1981), 190–203.

    Article  MathSciNet  MATH  Google Scholar 

  • KOSTREVA, M. M. 1. Direct Algorithms for Complementarity Problems. Rensselaer Polytechnic Institute, Troy, Ph. D. Dissertation, New York, (1976).

    Google Scholar 

  • KOSTREVA, M. M. 2. Block pivot methods for solving the complementarity problem. Linear Algebra Appl. 21 (1978), 207–215.

    Article  MathSciNet  MATH  Google Scholar 

  • KOSTREVA, M. M. 3. Cycling in linear complementarity problems. Math. Programming 16 (1979), 127–130.

    Article  MathSciNet  MATH  Google Scholar 

  • KOSTREVA, M. M. 4. Finite test sets and P-matrices. Proc. Amer. Math. Soc. 84 (1982), 104–105.

    MathSciNet  MATH  Google Scholar 

  • KOSTREVA, M. M. 5. Elasto-hydrodynamic lubrication: a nonlinear complementarity problem. International J. Numerical Meth. in Fluids, 4 (1984), 377–397.

    Article  MathSciNet  MATH  Google Scholar 

  • KOSTREVA, M. M. 6. Recent results on complementarity models for engineering and economics. Infor. 28 (1990), 324–334.

    MATH  Google Scholar 

  • LEMKE, C. E. 1. Bimatrix equilibrium points and mathematical programming. Management Science, 11 (1965), 681–689.

    MathSciNet  MATH  Google Scholar 

  • LEMKE, C. E. 2. On complementarity pivot theory. In: Mathematics of Decision Sciences, Part 1, (G. B. Dantzig, A. F. Veinott, Jr. (Eds.)) Ams, Providence, Rhode Island, (1968), 95–114.

    Google Scholar 

  • LEMKE, C. E. 3. Recent results on complementarity problems. In: Nonlinear Programming, (J. B. Rosen, O. L. Mangasarian and K. Ritter, (Eds.)), Academic Press. New York (1970), 349–384.

    Google Scholar 

  • LEMKE, C. E. 4. Some pivot schemes for the linear complementarity problem. Math. Programming Study 7 (1978), 15–35.

    Article  MathSciNet  MATH  Google Scholar 

  • LEMKE, C. E. 5. A brief survey of complementarity theory. In: Constructive Approaches to Mathematical Models, (C. V. Coffman and G. J. Fix (Eds.)), Academic Press, New York, (1979).

    Google Scholar 

  • LEMKE, C. E. 6. A survey of complementarity theory. In: Variational Inequalities and Complementarity Problems, (R. W. Cottle, F. Giannessi and J. L. Lions (Eds.)), John Wiley & Sons, (1980), 213–239.

    Google Scholar 

  • LEMKE, C. E. and HOWSON, J. T. 1. Equilibrium points of bimatrix games. Siam J. Appl. Math. 12 (1964), 413–423.

    Article  MathSciNet  MATH  Google Scholar 

  • MAIER, G. 1. A matrix structural theory of piecewise-linear elastoplasticity with interacting yield-planes. Meccanica 5 (1970), 54–66.

    Article  MATH  Google Scholar 

  • MAIER, G. 2. Problem on parametric linear complementarity problem. Siam Rev., 14 Nr. 2 (1972), 364–365.

    Article  MathSciNet  Google Scholar 

  • MAIER, G., ANDREUZZI, F., GIANNESSI, F., JURINA, L. and TADDEI, F. 1. Unilateral contact, elastoplasticity and complementarity with references to offshore pipeline design. Comput. Methods Appl. Mech. and Engineering, 17/18 (1979), 469–495.

    Article  Google Scholar 

  • MANDELBAUM, A. 1. The dynamic complementarity problem. Preprint, Graduate School of Business, Stanford University, Stanford, Ca. 94305, Usa (1990).

    Google Scholar 

  • MANGASARIAN, O. L. 1. Linear complementarity problems solvable by a single linear program. Math. Programming 10 (1976), 263–270.

    Article  MathSciNet  MATH  Google Scholar 

  • MANGASARIAN, O. L. 2. Solution of linear complementarity problems by linear programming. In: Numerical Analysis, (Gi. W. Watson, (Ed.)), Lecture Notes in Mathematics, Nr. 506, Springer-Verlag (1976), 166–175.

    Chapter  Google Scholar 

  • MANGASARIAN, O. L. 3. Equivalence of the complementarity problem to a system of nonlinear equations. Siam J. Appl. Math., 31 (1976), 89–92.

    Article  MathSciNet  MATH  Google Scholar 

  • MANGASARIAN, O. L. 4. Solution of symmetric linear complementarity problems by iterative methods. J. Opt. Theory Appl. 22 (1977), 465–485.

    Article  MathSciNet  MATH  Google Scholar 

  • MANGASARIAN, O. L. 5. Characterization of linear complementarity problems as linear programs. Math. Programming Study, 7 (1978), 74–87.

    Article  MathSciNet  MATH  Google Scholar 

  • MANGASARIAN, O. L. 6. Generalized linear complementarity problems as linear programs. In: Methods of Operations Research, (W. Oettli and F. Steffens (Eds.)), 31 (1979), 393–402.

    Google Scholar 

  • MANGASARIAN, O. L. 7. Simplified characterizations of linear complementarty problems solvable as linear programs. Math. Oper. Research 4 (1979), 268–273.

    Article  MathSciNet  MATH  Google Scholar 

  • MANGASARIAN, O. L. 8. Locally unique solutions of quadratic programs. linear and nonlinear complementarity problems. Math. Programming 19 (1980), 200–212.

    Article  MathSciNet  MATH  Google Scholar 

  • MANGASARIAN, O. L. 9. Characterization of bounded solutions of linear complementarity problems. Math. Programming Study. 19 (1982), 153–166.

    Article  MathSciNet  Google Scholar 

  • MANGASARIAN, O. L. 10. Simple computable bounds for solutions of linear complementarity problems and linear programs. Math. Programming Study, 2 5 (1985), 1–12.

    Article  MathSciNet  Google Scholar 

  • MANGASARIAN, O. L. 11. Error bounds for nondegenerate monotone linear complementarity problems. Math. Programming, Series B, 48 (1990), 437–445.

    Article  MathSciNet  MATH  Google Scholar 

  • MANGASARIAN, O. L. 12. Least norm solution of non-monotone linear complementarity problems. In: Functional Analysis, Optimization and Mathematical Economics, (L. J. Leifman, (Ed.)), Oxford University Press, Oxford (1990), 217–221.

    Google Scholar 

  • MANGASARIAN, O. L. 13. Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem. Siam J. Opt. 1 (1991), 114–122.

    Article  MathSciNet  MATH  Google Scholar 

  • MANGASARIAN, O. L. and PANG, J. S. 1. The extended linear complementarity problem. Siam J. Matrix Analysis Appl. 16 (12) (1995), 359–368.

    Article  MathSciNet  MATH  Google Scholar 

  • MCLINDEN, L. 1. The complementarity problem for maximal monotone multifunctions. In: Variational Inequalities and Complementarity Problems, (R. W. Cottle, F. Giannessi and J. L. Lions (Eds.)), John Wiley & Sons, (1980), 251–270.

    Google Scholar 

  • MCLINDEN, L. 2. An analogue ofMoreau’s proximation theorem with application to the nonlinear complementarity problem. Pacific J. Math. 88 Nr. 1, (1980) 101–161.

    Article  MathSciNet  MATH  Google Scholar 

  • MEISTER, H. 1. A parametric approach to complementarity theory. J. Math. Anal. Appl. 101, (1984), 64–77.

    Article  MathSciNet  MATH  Google Scholar 

  • MEGIDDO, N. 1. On monotonicity in parametric linear complementarity problems. Math. Programming, 12 (1966), 60–66.

    Article  MathSciNet  Google Scholar 

  • MEGIDDO, N. 2. A monotone complementarity problem with feasible solutions but no complementarity solutions. Math. Programming Study, 12 Nr. 1 (1977), 131–132.

    Article  MathSciNet  MATH  Google Scholar 

  • MEGIDDO, N. 3. On the parametric nonlinear complementarity problem. Math. Programming Study 7 (1978), 142–150.

    Article  MathSciNet  MATH  Google Scholar 

  • MEGIDDO, N. and KOJIMA, M. 1. On the existence and uniqueness of solutions in nonlinear complementarity theory. Math. Programming 12 (1977), 110–130.

    Article  MathSciNet  MATH  Google Scholar 

  • MOHAN, S. R. and NEOGY, S. K. 1. Algorithms for the generalized linear complementarity problem with a vertical block Z-matrix. Siam J. Optimization 6, Nr. 4 (1996), 994–1006.

    Article  MathSciNet  MATH  Google Scholar 

  • MOHAN, S. R., NEOGY, S. K. and SRIDHAR, R. 1. The generalized linear complementarity problem revisited. Math. Program-ming 74 (1996), 197–218.

    MathSciNet  MATH  Google Scholar 

  • MONTEIRO, R. D. C. and PANG, J. S. 1. On two interior-point mappings for nonlinear semidefinite complementarity problems. (Preprint) (1966), School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, 30332–0205.

    Google Scholar 

  • MORé, J. J. 1. Classes of functions and feasibility conditions in nonlinear complementarity problems. Math. Programming 6, (1974), 327–338.

    Article  MathSciNet  MATH  Google Scholar 

  • MORé, J. J. 2. Coercivity conditions in nonlinear complementarity problems. Siam Rev. 16, Nr. 1 (1974), 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  • MORé, J. J. and RHEINBOLDT, W. 1. On P-and S-functions and related classes of n-dimensional nonlinear mappings. Linear Algebra and Appl. 6 (1973), 45–68.

    Article  MathSciNet  MATH  Google Scholar 

  • MOSCO, U. 1.On some non-linear quasi-variational inequalities and implicit complemen-tarity problems in stochastic control theory. In: Variational Inequalities and Complementarity Problems. Theory and Applications. (R. W. Cottle, F. Giannessi and J. L. Lions (Eds.)), John Wiley & Sons (1980), 271–283.

    Google Scholar 

  • MOSCO, U. and SCARPINI, F. 1. Complementarity systems and approximation of variational inequalities. Rairo Recherche Oper. (Analyse Numer.), (1975), 83–104.

    Google Scholar 

  • MURTY, K. G. 1. On the Number of Solutions to the Complementarity Quadratic Programming Problem. Doctoral Dissertation, Engineering Science, University of California, Berkeley, (1968).

    Google Scholar 

  • MURTY, K. G. 2. On the characterization ofP-matrices. Siam J. Appl. Math. 20 (3), (1971), 378–384.

    MATH  Google Scholar 

  • MURTY, K. G. 3. On the number of solutions to the complementarity problem and the spanning properties of complementarity cones. Linear Algebra Appl. 5 (1972) 65–108.

    Article  MATH  Google Scholar 

  • MURTY, K. G. 4. On the Bard-type scheme for solving the complementarity problem. Opsearch 11 (1974), 123–130.

    MathSciNet  Google Scholar 

  • MURTY, K. G. 5. On the linear complementarity problem. Oper. Research Verfahren 31 (1978), 425–439.

    Google Scholar 

  • MURTY, K. G. 6. Computational complexity of complementarity pivot methods. Math. Program-ming Study 7 (1978), 61–73 .

    Article  MATH  Google Scholar 

  • MURTY, K. G. 7. Linear Complementarity, Linear and Nonlinear Programming. Heldermann Verlag, Berlin (1988).

    MATH  Google Scholar 

  • OH, K. P. 1. The formulation of the mixed lubrication problem as a generalized nonlinear complementarity problem. J. Tribology 108 (1986), 598–604.

    Article  Google Scholar 

  • PANG, J. S. 1. Least Element Complementarity Theory. Ph. D. Thesis, Department of Opera-tions Research, Stanford University, Stanford, California (1976).

    Google Scholar 

  • PANG, J. S. 2.A note on an open problem in linear complementarity. Math. Programming 13 (1977), 360–363.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S. 3. On cone ordering and the linear complementarity problem. Linear Algebra Appl. 22 (1978), 267–281.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S. 4. On a class of least-element linear complementarity problems. Math. Programming 16 (1979), 111–126.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S. 5. On Q-matrices. Math. Programming 17 (1979), 243–247.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S. 6. Hidden Z-matrices with positive principal minors. Linear Algebra Appl. 23 (1979), 201–215.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S. 7. A parametric linear complementarity technique for optimal portfolio selection with a risk-free asset. Oper. Research 28 (1980), 927–941.

    Article  MATH  Google Scholar 

  • PANG, J. S. 8. A unification of two classes of Q-matrices. Math. Programming 20 (1981), 348–352.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S. 9. The implicit complementarity problem. In: Nonlinear Programming 4, (Mangassarian, O. L., Meyer R. R. and Robinson S. M., (Eds.)), Academic Press, New York (1981), 487–518.

    Google Scholar 

  • PU J. S. 10. On the convergence of a basic iterative method for the implicit complementarity problem. J. Opt. Theory Appl. 37 (1982), 149–162.

    Article  MATH  Google Scholar 

  • PANG, J. S. 11. Necessary and sufficient conditions for the convergence of iterative methods for the linear complementarity problem. J. Opt. Theory Appl. 42 (1984), 1–17.

    Article  MATH  Google Scholar 

  • PANG, J. S. 12. More results on the convergence of iterative methods for the symmetric linear complementarity problems. J. Opt. Theory Appl. 49 (1986), 107–134.

    Article  MATH  Google Scholar 

  • U. S. 13. Inexact Newton methods for the nonlinear complementarity problem. Math. Programming 36 (1986), 54–71.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S. 14. Two characterization theorems in complementarity theory. Oper. Research Letters 7 (1988), 27–31.

    Article  MATH  Google Scholar 

  • PANG, J. S. 15. Iterative descent algorithms for a row sufficient linear complementarity problem. Siam J. Matrix Anal. Appl. 12 (1991), 611–624.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S. 16. A B-differentiable equation based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems. Math. Programming 51 (1991), 101–132.

    Article  MathSciNet  MATH  Google Scholar 

  • PANG, J. S.17. Complementarity problems. In: Handbook in Global Optimization, (Horst R. and Pardalos P. (Eds.)), Kluwer Academic Publishers, Boston (1994), 271–338.

    Google Scholar 

  • PETERSON, W. P. 1. Diffusion Approximations for Networks of Queues with Multiple Customer Types. Ph. D. Thesis, Dept. of Operations Research, Stanford University, Ca. (1985).

    Google Scholar 

  • REIMAN, M. I. 1. Open queuing networks in heavy traffic. Math. Oper. Research 9 (1984), 441–458.

    Article  MathSciNet  MATH  Google Scholar 

  • SAIGAL, R. 1. A note on a class of linear complementarity problem. Opsearch 7 (1970), 175–183.

    MathSciNet  Google Scholar 

  • SAIGAL, R. 2 Lemke’s algorithm and a special linear complementarity problem. Opsearch 8 (1971), 201–208.

    MathSciNet  Google Scholar 

  • SAIGAL, R. 3. On the class of complementarity cones and Lemke’s algorithm. Siam J. Appl. Math. 23 Nr. 1 (1972). 46–60.

    MathSciNet  MATH  Google Scholar 

  • SAIGAL, R. 4. A characterization of the constant parity property of the number of solutions to the linear complementaritv problem. Siam J. Appl. Math. 23 (1972), 40–45.

    MathSciNet  MATH  Google Scholar 

  • SAIGAL, R. 5. Extension of the generalized complementarity problem. Math. Oper. Research 1 Nr. 3 (1976), 260–266.

    Article  MathSciNet  MATH  Google Scholar 

  • SUN, M. 1. Monotonicity of Mangasarian’s iterative algorithm for generalized linear complementarity problems. J. Math. Anal. Appl. 144 (1989), 474–485.

    Article  MathSciNet  MATH  Google Scholar 

  • SZANC, B. P. 1. The Generalized Complementarity Problem. Ph. D. Thesis, Rensselaer Polytechnic Institute, Troy, N. Y. (1989).

    Google Scholar 

  • SZNAJDER, R. 1. Degree Theoretic Analysis of the Vertical and Horizontal Linear Complemen-tarity Problem. Ph. D. Thesis, University of Maryland (1994).

    Google Scholar 

  • SZNAJDER, R. and GOWDA, M. S. 1. Generalizations of P 0 - and P-properties; extended vertical and horizontal linear complementarity problems. Linear Algebra and its Application. 223/224, (1995), 695–715.

    Google Scholar 

  • TAMIR, A. 1. Minimality and complementarity properties associated with Z-functions and M-functions. Math. Programming, 7 (1974), 17–31.

    Article  MathSciNet  MATH  Google Scholar 

  • VESCAN, R. T. 1. Un problème variationnel implicite faible. C. R. Acad. Sci. Paris, t. 299, Serie A Nr. 14 (1984), 655–658.

    MathSciNet  Google Scholar 

  • VESCAN, R. T. 2. A weak implicit variational inequality. Preprint, Al. I. Cuza University. Iasi (Romania) (1994)

    Google Scholar 

  • WALRAS, L. 1. Elements of Pure Economics. Allen and Unwin, London (1954).

    Google Scholar 

  • WENECOUR, M. 1. A Production Network Model and its Diffusion Limit. Ph. D. Thesis, Statistics Department, Stanford University, Ca. (1982)

    Google Scholar 

  • WINTGEN, G. 1. Indifferente optimierungs probleme. In: Beitrag zur Internationalen Tagung. Mathematik und Kybernetik in der Okonomie, Berlin (1964), Konferenz-protocoll, Teil Ii, (Akademie Verlag, Berlin), 3–6.

    Google Scholar 

  • YANG, P. 1. Pathwise Solution for a Class ofLinear Stochastic Systems. Ph. D. Thesis, Department of Operations Research, Stanford University , Ca. (1988).

    Google Scholar 

  • YE, Y. 1. A fully polynomial-time approximation algorithm for computing a stationary point of the general linear complementarity problem. Math. Oper. Research 18 (2), (1993), 334–345.

    Article  MATH  Google Scholar 

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Isac, G. (2000). Complementarity Problems. Origins and Definitions. In: Topological Methods in Complementarity Theory. Nonconvex Optimization and Its Applications, vol 41. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3141-5_2

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