Multiobjective programming with semilocally convex functions
type: Item
instance of: scholarly article
title: Multiobjective programming with semilocally convex functions
zbMATH Open document ID: 0864.90111
author: R. N. Mukherjee
author: S. K. Mishra
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-01-01T00:00:00Z
review text: Multiobjective programming, in recent times, has become an important area of investigation. We try to show naturally some of the uses of the class of semilocally convex functions in dealing with optimality conditions and duality theory as applied for treating a multiobjective mathematical program. The concept of semilocal convexity was introduced by G. M. Ewing (1977) who applied it to derive sufficient optimality conditions for variational and control problems. Semilocally convex functions have certain important convex type properties, e.g., local minima of semilocally convex functions defined on locally star-shaped sets are also global minima, and nonnegative linear combinations of semilocally convex functions are also semilocally convex. In Section 2 we introduce certain notations and mention the key lemmas which were relevant for single objective programming problems [see \textit{T. Weir}, ibid. 168, 1-12 (1992; Zbl 0762.90064)]. In the same section, some lemmas are given as statements in a different format. Finally, we state the alternative theorem derived by Weir which is an important proposition for deducing necessary optimality conditions. In Section 3 we introduce a multiobjective programming problem and we derive necessary saddle-point criteria for optimality for a semilocally convex program. Section 4 deals with Kuhn-Tucker necessary optimality conditions, sufficient optimality conditions, and duality for a semilocally convex multiobjective program. Some applications have been given in Section 5 for a multiobjective program with fractional objectives.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C32
zbMATH DE Number: 902550
zbMATH Keywords: multiobjective programming
zbMATH Keywords: semilocally convex functions
zbMATH Keywords: optimality conditions
zbMATH Keywords: duality theory
zbMATH Keywords: alternative theorem
zbMATH Keywords: saddle-point criteria
zbMATH Keywords: Kuhn-Tucker necessary optimality conditions
zbMATH Keywords: duality
zbMATH Keywords: fractional objectives
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0150
OpenAlex ID: W1991564992
DOI: 10.1006/JMAA.1996.0150
description: scientific article; zbMATH DE number 902550