• G. Isac
  • V. A. Bulavsky
  • V. V. Kalashnikov
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 63)


To a certain degree, the concept of complementarity is analogous to the concept of a stationary point in the extremum problems.If the point z̄ is a (local) minimum of a real differentiable function / defined over the positive half-axis R + = [0,+∞] then the inequality f’(0) ≥ 0 is the necessary condition of that.


Variational Inequality Linear Form Interior Point Complementarity Problem Nonlinear Complementarity Problem 
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  1. Cottle RW, Dantzig GB. A generalization of the linear complementarity problem. J.j of Combinatorial Theory 1970; 8: 79–90. IMathSciNetzbMATHCrossRefGoogle Scholar
  2. Cottle, R.W., Giannessi, F., Lions, J.-L. (eds). Variational inequalities and complementarity problems. New York: Academic Press, 1980.zbMATHGoogle Scholar
  3. Farkas J. Uber die Theorie der einfachen Ungleichungen. J. Reine Angew. Math. 1902; 124: 1–24.Google Scholar
  4. Harker PT, Pang J-S. Finite-dimensional variational inequalities and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Programming 1990; 48: 161–220.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Isac, G. Complementarity Problems. Lecture Notes in Mathematics. Berlin-Heidelberg: Springer-Verlag, 1992.zbMATHGoogle Scholar
  6. Isac G, Bulavsky VA, Kalashnikov VV. Exceptional families, topological degree and complementarity problems. J. Global Optim. 1997; 10: 207–225.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Karamardian S. The complementarity problem. Math. Programming 1972; 2: 107–129.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Lemke CE, Howson JJ. Equilibrium points of bimatrix games. SIAM J. 1964; 12: 413–423.MathSciNetzbMATHGoogle Scholar
  9. Lions, J.-L. 1. Controle optimal de syst&mes gouvernhs par des Equations aux diriv6es partielles Paris, 1968.Google Scholar
  10. Lions, J.-L. 2. Quelques m€thodes de resolution des probl&mes aux limites non lineares Paris, 1969.Google Scholar
  11. More JJ. Coercivity conditions in nonlinear complementarity problems. Math. [Programming] 1974; 5: 327–338. IMathSciNetGoogle Scholar
  12. Motzkin, T.S, Beitrage zur Theorie der linearen Ungleichungen. (Dissertation, Basel, 1933), Jerusalem, 1936.Google Scholar
  13. von Neumann, J., and Morgenstern, O. Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1944.zbMATHGoogle Scholar
  14. Nikaido, H. Convex Structures and Economic Theory. New York — London: Academic Press, 1968.zbMATHGoogle Scholar
  15. Ortega, J.M, Rheinboldt, W.C. Iterative Solutions of Nonlinear Equations of Several Variables. New York — London: Academic Press, 1970.Google Scholar
  16. Tucker, A.W. “Dual systems of homogeneous linear relations”.-In: Linear Inequalities and Related Systems, H.W. Kuhn and A.W. Tucker, eds. Princeton: Princeton University Press, 1956.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • G. Isac
    • 1
  • V. A. Bulavsky
    • 2
  • V. V. Kalashnikov
    • 2
  1. 1.Department of Mathematics and Computer ScienceRoyal Military College of CanadaKingstonCanada
  2. 2.Central Economics Institute (CEMI) of Russian Academy of SciencesMoscowRussia

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