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.
Similar content being viewed by others
References
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.
J.E. Falk and R.M. Soland, “An algorithm for separable nonconvex programming probblems”,Management Science 15(9) (1969) 550–569.
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).
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.
R.M. Soland, “An algorithm for separable nonconvex programming problems II: nonconvex constraints”,Management Science 17(11) (1971) 759–773.
Author information
Authors and Affiliations
Additional information
This work was supported by Contract AFORS-73-2504, U.S. Air Force, Office of Scientific Research.
Rights and permissions
About this article
Cite this article
McCormick, G.P. Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems. Mathematical Programming 10, 147–175 (1976). https://doi.org/10.1007/BF01580665
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01580665