First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

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 -