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Title: First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints
Authors: Ginchev, Ivan
Ivanov, Vsevolod I.
Keywords: Nonsmooth Optimization
Dini Directional Derivatives
Quasiconvex Functions
Pseudoconvex Functions
Quasiconvex Programming
Kuhn-Tucker Conditions
Issue Date: 2008
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 34, No 3, (2008), 607p-618p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.
ISSN: 1310-6600
Appears in Collections:Volume 34, Number 3

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