Generalized Affine Functions and Generalized Differentials

Linh, Nguyen Thi Hong; Penot, Jean-Paul

doi:10.1007/s10957-012-0051-4

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“…The case of pseudo-a¢ ne functions (also called pseudo-linear functions) is studied elsewhere ( [23]) with similar concepts and methods. It requires some results of the present paper.…”

Section: Introductionmentioning

confidence: 99%

Generalized convex functions and generalized differentials

Linh

Penot

2011

Optimization

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We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced. We devise some optimality conditions for constrained optimization problems. In particular, we get Lagrange-KuhnTucker multipliers for mathematical programming problems.

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“…The case of pseudo-a¢ ne functions (also called pseudo-linear functions) is studied elsewhere ( [23]) with similar concepts and methods. It requires some results of the present paper.…”

Section: Introductionmentioning

confidence: 99%