Nonlinear extensions of Farkas' lemma with applications to global optimization and least squares

Nonlinear extensions of Farkas' lemma with applications to global optimization and least squares

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Article ID: iaor20041835
Country: United States
Volume: 20
Issue: 4
Start Page Number: 818
End Page Number: 837
Publication Date: Nov 1995
Journal: Mathematics of Operations Research
Authors: ,
Abstract:

A nonlinear extension of Farkas' lemma for systems involving the difference of sublinear functions is presented. This extension of Farkas' lemma is applied to give a complete characterization of global optimality for constrained global optimization problems in which the objective function is the difference of a convex and sublinear function and the constraints are systems of difference sublinear functions. An application to certain fractional programming problems is also given. These results are achieved with merely a stronger consistency condition which reduces to the usual feasibility requirement for problems with sublinear constraints. Further generalizations of Farkas' lemma for systems involving convex and difference sublinear functions are also presented. Moreover, a generalized Farkas' lemma for certain specially structural convex inequality systems is shown to be related to the solution of appropriate constrained least squares problems.

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