Mathematical Programming

, Volume 10, Issue 1, pp 147–175 | Cite as

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

  • Garth P. McCormick


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.


Mathematical Method Programming Problem Global Minimizer Nonlinear Programming Global Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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    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
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    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
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    R.M. Soland, “An algorithm for separable nonconvex programming problems II: nonconvex constraints”,Management Science 17(11) (1971) 759–773.MathSciNetCrossRefzbMATHGoogle 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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