# First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

Ginchev, Ivan; Ivanov, Vsevolod I.

Serdica Mathematical Journal (2008)

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

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topGinchev, 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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