First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

• Volume: 34, Issue: 3, page 607-618
• ISSN: 1310-6600

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Abstract

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2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally dependent multipliers. The two cases, where the Lagrange function satisfies a non-strict and a strict inequality, are considered. In the case of a non-strict inequality pseudoconvex functions are involved and in their terms some properties of the convex programming problems are generalized. The efficiency of the obtained conditions is illustrated on examples.

How to cite

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Ginchev, Ivan, and Ivanov, Vsevolod I.. "First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints." Serdica Mathematical Journal 34.3 (2008): 607-618. <http://eudml.org/doc/281480>.

@article{Ginchev2008,
abstract = {2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally dependent multipliers. The two cases, where the Lagrange function satisfies a non-strict and a strict inequality, are considered. In the case of a non-strict inequality pseudoconvex functions are involved and in their terms some properties of the convex programming problems are generalized. The efficiency of the obtained conditions is illustrated on examples.},
author = {Ginchev, Ivan, Ivanov, Vsevolod I.},
journal = {Serdica Mathematical Journal},
keywords = {Nonsmooth Optimization; Dini Directional Derivatives; Quasiconvex Functions; Pseudoconvex Functions; Quasiconvex Programming; Kuhn-Tucker Conditions; nonsmooth optimization; Dini directional derivatives; quasiconvex functions; pseudoconvex functions; quasiconvex programming; Kuhn-Tucker conditions},
language = {eng},
number = {3},
pages = {607-618},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints},
url = {http://eudml.org/doc/281480},
volume = {34},
year = {2008},
}

TY - JOUR
AU - Ginchev, Ivan
AU - Ivanov, Vsevolod I.
TI - First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints
JO - Serdica Mathematical Journal
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 34
IS - 3
SP - 607
EP - 618
AB - 2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally dependent multipliers. The two cases, where the Lagrange function satisfies a non-strict and a strict inequality, are considered. In the case of a non-strict inequality pseudoconvex functions are involved and in their terms some properties of the convex programming problems are generalized. The efficiency of the obtained conditions is illustrated on examples.
LA - eng
KW - Nonsmooth Optimization; Dini Directional Derivatives; Quasiconvex Functions; Pseudoconvex Functions; Quasiconvex Programming; Kuhn-Tucker Conditions; nonsmooth optimization; Dini directional derivatives; quasiconvex functions; pseudoconvex functions; quasiconvex programming; Kuhn-Tucker conditions
UR - http://eudml.org/doc/281480
ER -

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