Lagrange multiplier theorem of multiobjective programming problems with set functions
type: Item
instance of: scholarly article
title: Lagrange multiplier theorem of multiobjective programming problems with set functions
zbMATH Open document ID: 0741.90058
DOI: 10.1007/BF00940508
author: S. Singh
published in: Journal of Optimization Theory and Applications
publication date: 1992-06-25T00:00:00Z
review text: The authors consider a class of multiobjective programming problems with set functions in which the domination structure does not necessarily contain the nonnegative orthant. First, a generalized Farkas-Minkowski theorem for set functions is proved. As a consequence, a Lagrange multipliers theorem is obtained for the case of single objective programming problems with set functions. Next, with a scalarization proposition, the result is extended to the case of multiobjective programming problems with set functions under the hypotheses of a generalized Slater's constraint qualification and of a restriction to proper efficiency. The authors also relate proper efficient solutions to the zero-like functions associated with the subdifferentials of the set functions involved, which presents a new perspective for a proper efficient solution.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 26E25
zbMATH DE Number: 12587
zbMATH Keywords: multiobjective programming
zbMATH Keywords: set functions
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: proper efficiency
zbMATH Keywords: subdifferentials
reviewed by: Shouyang Wang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 12587