DUALITY IN DISCRETE PROGRAMMING. 3. NONLINEAR OBJECTIVE FUNCTION AND CONSTRAINTS

Abstract

The results of 'Duality in Discrete Programming,' are extended in this paper (which, however, is self-contained) to the case of dual programs with nonlinear objective function and nonlinear constraints. The symmetric dual nonlinear programs studied by Dantzig, Eisenberg and Cottle, as well as the dual nonlinear programs formulated by Wolfe, Mangasarian and Huard are generalized by allowing some of the variables to be constrained to belong to arbitrary sets of real numbers, and dropping the requirement that the objective function and the constraints be convex (concave) in these variables. The basic properties established for the above problems are shown to carry over, with some qualification, to their generalized counterparts which encompass, among others, various types of mixed-integer nonlinear programs.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1968
Accession Number
AD0666627

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  • Egon Balas

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  • Carnegie Mellon University

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