Mathematical Programming

, Volume 10, Issue 1, pp 147–175

Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems

  • Garth P. McCormick
Article

Abstract

For nonlinear programming problems which are factorable, a computable procedure for obtaining tight underestimating convex programs is presented. This is used to exclude from consideration regions where the global minimizer cannot exist.

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References

  1. [1]
    E.M.L. Beale and J.A. Tomlin, “Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables”, in: J. Laurence, ed.,Proceedings of the fifth international conference on operational research (Tavistock Publications, London, 1970) pp. 447–454.Google Scholar
  2. [2]
    J.E. Falk and R.M. Soland, “An algorithm for separable nonconvex programming probblems”,Management Science 15(9) (1969) 550–569.CrossRefMATHGoogle Scholar
  3. [3]
    G.P. McCormick, “Converting general nonlinear programming problems to separable nonlinear programming problems”, Technical Paper Serial T-267, Program in Logistics, The George Washington University, Washington, D.C. (1972).Google Scholar
  4. [4]
    G.P. McCormick, “Attempts to calculate global solutions of problems that may have local minima”, in: F.A. Lootsma, ed.,Numerical methods for nonlinear optimization (Academic Press, New York, 1972) pp. 209–221.Google Scholar
  5. [5]
    R.M. Soland, “An algorithm for separable nonconvex programming problems II: nonconvex constraints”,Management Science 17(11) (1971) 759–773.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Mathematical Programming Society 1976

Authors and Affiliations

  • Garth P. McCormick
    • 1
  1. 1.The George Washington UniversityWashington, D.C.USA

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