Strict minimizers of order m in nonsmooth optimization problems

Tadeusz Antczak; Krzysztof Kisiel

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 2, page 213-232
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Antczak, Tadeusz, and Kisiel, Krzysztof. "Strict minimizers of order $m$ in nonsmooth optimization problems." Commentationes Mathematicae Universitatis Carolinae 47.2 (2006): 213-232. <http://eudml.org/doc/249854>.

@article{Antczak2006,
abstract = {In the paper, some sufficient optimality conditions for strict minima of order $m$ in constrained nonlinear mathematical programming problems involving (locally Lipschitz) $(F,\rho )$-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.},
author = {Antczak, Tadeusz, Kisiel, Krzysztof},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonsmooth programming; strict local minimizer of order $m$; Clarke’s generalized gradient; $(F, \rho )$-convex function of order $m$ with respect to $\theta $; nonsmooth programming; strict local minimizer of order },
language = {eng},
number = {2},
pages = {213-232},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Strict minimizers of order $m$ in nonsmooth optimization problems},
url = {http://eudml.org/doc/249854},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Antczak, Tadeusz
AU - Kisiel, Krzysztof
TI - Strict minimizers of order $m$ in nonsmooth optimization problems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 2
SP - 213
EP - 232
AB - In the paper, some sufficient optimality conditions for strict minima of order $m$ in constrained nonlinear mathematical programming problems involving (locally Lipschitz) $(F,\rho )$-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.
LA - eng
KW - nonsmooth programming; strict local minimizer of order $m$; Clarke’s generalized gradient; $(F, \rho )$-convex function of order $m$ with respect to $\theta $; nonsmooth programming; strict local minimizer of order
UR - http://eudml.org/doc/249854
ER -

References

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