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.

On the separation of parametric convex polyhedral sets with application in MOLP

Milan Hladík (2010)

Applications of Mathematics

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We investigate diverse separation properties of two convex polyhedral sets for the case when there are parameters in one row of the constraint matrix. In particular, we deal with the existence, description and stability properties of the separating hyperplanes of such convex polyhedral sets. We present several examples carried out on PC. We are also interested in supporting separation (separating hyperplanes support both the convex polyhedral sets at given faces) and permanent separation...