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GLOPT — A Program for Constrained Global Optimization

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Developments in Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 18))

Abstract

GLOPT is a Fortran77 program for global minimization of a block-separable objective function subject to bound constraints and block-separable constraints. It finds a nearly globally optimal point that is near a true local minimizer. Unless there are several local minimizers that are nearly global, we thus find a good approximation to the global minimizer.

GLOPT uses a branch and bound technique to split the problem recursively into subproblems that are either eliminated or reduced in their size. This is done by an extensive use of the block separable structure of the optimization problem.

In this paper we discuss a new reduction technique for boxes and new ways for generating feasible points of constrained nonlinear programs. These are implemented as the first stage of our GLOPT project. The current implementation of GLOPT uses neither derivatives nor simultaneous information about several constraints. Numerical results are already encouraging. Work on an extension using curvature information and quadratic programming techniques is in progress.

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References

  1. A. B. Babichev, O. B. Kadyrova, T. P. Kashevarova, A. S. Leshchenko, and A. L. Semenov, UniCalc, a novel approach to solving systems of algebraic equations, Interval Computations 3 (1993), 29–47.

    MathSciNet  Google Scholar 

  2. F. Benhamou and W. J. Older, Applying interval arithmetic to real, integer, and boolean constraints, J. of Math. Mech., 1995.

    Google Scholar 

  3. S. Berner, New results on verified global optimization, submitted 1995.

    Google Scholar 

  4. H. M. Chen and M. H. van Emden, Adding interval constraints to the Moore-Skelboe global optimization algorithm, pp. 54–57 in: V. Kreinovich (ed.) Extended Abstracts of APIC’95, International Workshop on Applications of Interval Computations, Reliable Computing (Supplement), 1995.

    Google Scholar 

  5. T. Csendes and D. Ratz, Subdivision direction selection in interval methods for global optimization, SIAM J. Numer. Anal., to appear.

    Google Scholar 

  6. L. Davis (ed.), Handbook of genetic algorithms, van Nostrand Reinhold, New York 1991.

    Google Scholar 

  7. J.E. Dennis Jr., D.M. Gay, and R.E. Welsch, Algorithm 573. NL2SOL — An adaptive nonlinear least-squares algorithm, ACM Trans. Math. Softw. 7 (1981), 369–383.

    Article  Google Scholar 

  8. L.C.W. Dixon and G.P. Szegö, Towards global optimization, Elsevier, New York 1975.

    Google Scholar 

  9. T. G. W. Epperly, Global optimization of nonconvex nonlinear programs using parallel branch and bound, PH. D. Thesis, Dept. of Chem. Eng., University of Wisconsin — Madison, 1995.

    Google Scholar 

  10. C. A. Floudas and P.M. Pardalos, A collection of test problems for constrained global optimization algorithms, Lecture Notes Comp. Sci. 455, Springer, Berlin 1990.

    Book  MATH  Google Scholar 

  11. G. D. Hager, Solving large systems of nonlinear constraints with application to data modeling, Interval Computations 3 (1993), 169–200.

    MathSciNet  Google Scholar 

  12. E. Hansen, Global optimization using interval analysis, Dekker, New York 1992.

    MATH  Google Scholar 

  13. J. Holland, Genetic algorithms and the optimal allocation of trials, SIAM J. Computing 2 (1973), 88–105.

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Horst and P.M. Pardalos (eds.), Handbook of global optimization, Kluwer 1995.

    MATH  Google Scholar 

  15. E. Hyvönen, Constraint reasoning based on interval arithmetic, In N. S. Sridharan (ed.), IJCAI-89 Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, 1989.

    Google Scholar 

  16. E. Hyvönen, Global consistency in interval constraint satisfaction, In B. Mayoh (ed.), Scandinavian Conference on Artificial Intelligence — 91. ‘Odin’s Ravens’. Proceedings of the SCAI ’91, 1991.

    Google Scholar 

  17. E. Hyvönen and S. De Pascale, Interval computations on the spreadsheet. pp. 169–209 in: R. B. Kearfott and V. Kreinovich (eds.), Applications of Interval Computations, Applied Optimization, Kluwer, Dordrecht 1996.

    Chapter  Google Scholar 

  18. C. Jansson, On self-validating methods for optimization problems, pp. 381–438 in: Topics in validated computations, (J. Herzberger, ed.): Elsevier Science B.V., 1994.

    Google Scholar 

  19. C. Jansson and O. Knüppel, A global minimization method: The multidimensional case, Preprint, 1992.

    Google Scholar 

  20. C. Jansson and O. Knüppel, Branch and bound algorithm for bound constrained optimization problems without derivatives, J. Global Optim. 7 (1995), 297–333.

    Article  MathSciNet  MATH  Google Scholar 

  21. R.B. Kearfott, M. Novoa and Chenyi Hu, A review of preconditioners for the interval Gauss-Seidel method, Interval Computations 1 (1991), 59–85.

    Google Scholar 

  22. R. B. Kearfott, Decomposition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems, Computing, 47 (1991), 169–191.

    Article  MathSciNet  MATH  Google Scholar 

  23. R.B. Kearfott, A review of techniques in the verified solution of constrained global optimization problems, to appear.

    Google Scholar 

  24. S. Kirkpatrick, C.D. Geddat Jr., and M.P. Vecchi, Optimization by simulated annealing, Science 220 (1983), 671–680.

    Article  MathSciNet  MATH  Google Scholar 

  25. A.V. Levy, and A. Montalvo, The tunneling algorithm for the global minimization of functions, SIAM J. Sci. Stat. Comput. 6 (1985), 15–29.

    Article  MathSciNet  MATH  Google Scholar 

  26. W. A. Lodwick, Constraint propagation, relational arithmetic in AI systems and mathematical programs, Ann. Oper. Res. 21 (1989), 143–148.

    Article  MATH  Google Scholar 

  27. C.D. Maranas and C.A. Floudas, Global minimum potential energy conformations of small molecules, J. Global Optim. 4 (1994), 135–170.

    Article  MathSciNet  MATH  Google Scholar 

  28. C.D. Maranas and Ch. A. Floudas, Finding all solutions of nonlinearly constrained systems of equations, J. Global Optim. 7 (1995), 143–182.

    Article  MathSciNet  MATH  Google Scholar 

  29. J. Mockus, Bayesian approach to global optimization, Kluwer, Dordrecht 1989.

    Book  MATH  Google Scholar 

  30. R.E. Moore, Methods and applications of interval analysis, SIAM, Philadelphia 1979.

    Book  MATH  Google Scholar 

  31. G.L. Nemhauser and L.A. Wolsey, Integer Programming, Chapter VI (pp. 447–527) in: Optimization (G.L. Nemhauser et al., eds.), Handbooks in Operations Research and Management Science, Vol. 1, North Holland, Amsterdam 1989.

    Chapter  Google Scholar 

  32. A. Neumaier, The enclosure of solutions of parameter-dependent systems of equations, pp. 269–286 in: Reliability in Computing (R.E. Moore, ed.), Acad. Press, San Diego 1988.

    Google Scholar 

  33. A. Neumaier, Interval methods for systems of equations, Cambridge Univ. Press, Cambridge 1990.

    MATH  Google Scholar 

  34. A. Neumaier, Second-order sufficient optimality conditions for local and global nonlinear programming, J. Global Optimization, to appear.

    Google Scholar 

  35. A. Neumaier, NOP — a compact input format for nonlinear optimization problems, This volume.

    Google Scholar 

  36. P.M Pardalos and J.B. Rosen, Constrained global optimization: Algorithms and applications, Lecture Notes in Computer Science 268, Springer, Berlin 1987.

    Book  MATH  Google Scholar 

  37. D. Ratz, On branching rules in second-order branch-and-bound methods for global optimization, in: G. Alefeld et al. (eds.), Scientific computation and validation, Akademie-Verlag, Berlin 1996.

    Google Scholar 

  38. D. Ratz and T. Csendes, On the selection of subdivision directions in interval branch-and-bound methods for global optimization, J. Global. Optim. 7 (1995) 183–207.

    Article  MathSciNet  MATH  Google Scholar 

  39. C.A. Schnepper and M.A. Stadtherr, Application of a parallel interval Newton/generalized bisection algorithm to equation-based chemical process flow-sheeting, Interval Computations 4 (1994), 40–64.

    Google Scholar 

  40. X. Shi, Intermediate Expression Preconditioning and Verification for Rigorous Solution of Nonlinear Systems, PhD thesis, University of Southwestern Louisiana, Department of Mathematics, August 1995.

    Google Scholar 

  41. A. Törn and A. Zilinskas, Global optimization, Lecture Notes in Computer Science 350, Springer, Berlin 1989.

    Book  MATH  Google Scholar 

  42. P. Van Hentenryck, Constraint Satisfaction in Logic Programming, MIT Press, Cambridge, MA, 1989.

    Google Scholar 

  43. P. Van Hentenryck, D. McAllester, and D. Kapur, Solving polynomial systems using a branch and prune approach, Technical Report CS-95–01, Dept. of Comp. Sci., Brown University, 1995.

    Google Scholar 

  44. G. Walster, E. Hansen and S. Sengupta, Test results for a global optimization algorithm, pp.272–287 in: Numerical optimization 1984 (P.T. Boggs et al., eds), SIAM, Philadelphia 1985.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    S. Dallwig, A. Neumaier & H. Schichl

Authors
  1. S. Dallwig
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  2. A. Neumaier
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  3. H. Schichl
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Editor information

Editors and Affiliations

  1. University of Vienna, Vienna, Austria

    Immanuel M. Bomze

  2. József Attila University, Szeged, Hungary

    Tibor Csendes

  3. University of Trier, Trier, Germany

    Reiner Horst

  4. University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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© 1997 Springer Science+Business Media Dordrecht

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Dallwig, S., Neumaier, A., Schichl, H. (1997). GLOPT — A Program for Constrained Global Optimization. In: Bomze, I.M., Csendes, T., Horst, R., Pardalos, P.M. (eds) Developments in Global Optimization. Nonconvex Optimization and Its Applications, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2600-8_2

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  • DOI: https://doi.org/10.1007/978-1-4757-2600-8_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4768-0

  • Online ISBN: 978-1-4757-2600-8

  • eBook Packages: Springer Book Archive

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