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Displaying similar documents to “ r –convex transformability in nonlinear programming problems”

Strict minimizers of order m in nonsmooth optimization problems

Tadeusz Antczak, Krzysztof Kisiel (2006)

Commentationes Mathematicae Universitatis Carolinae

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In the paper, some sufficient optimality conditions for strict minima of order m in constrained nonlinear mathematical programming problems involving (locally Lipschitz) ( F , ρ ) -convex functions of order m are presented. Furthermore, the concept of strict local minimizer of order m is also used to state various duality results in the sense of Mond-Weir and in the sense of Wolfe for such nondifferentiable optimization problems.

A d.c. C 1 function need not be difference of convex C 1 functions

David Pavlica (2005)

Commentationes Mathematicae Universitatis Carolinae

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In [2] a delta convex function on ℝ 2 is constructed which is strictly differentiable at 0 but it is not representable as a difference of two convex function of this property. We improve this result by constructing a delta convex function of class C 1 ( ℝ 2 ) which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable at 0.