On alternative theorems and necessary conditions for efficiency

In this article, we establish theorems of the alternative for a system described by inequalities, equalities and a set inclusion, which are generalizations of Tucker's classical theorem of the alternative, and develop Kuhn-Tucker necessary conditions for efficiency to mathematical programs in n...

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Bibliographic Details
Published inOptimization Vol. 58; no. 1; pp. 49 - 62
Main Authors Luu, Do Van, Hung, Nguyen Manh
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 01.01.2009
Taylor & Francis LLC
Taylor & Francis
Subjects
constraint qualification
Efficiency
Humanities and Social Sciences
Kuhn-Tucker necessary condition
Lagrange multiplier
Mathematical programming
Studies
theorem of the alternative
THEOREM OF THE ALTERNATIVE
MULTIOBJECTIVE OPTIMIZATION PROBLEMS
OPTIMALITY CONDITIONS
KUHN-TUCKER NECESSARY CONDITION
CONSTRAINT QUALIFICATION
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Summary:In this article, we establish theorems of the alternative for a system described by inequalities, equalities and a set inclusion, which are generalizations of Tucker's classical theorem of the alternative, and develop Kuhn-Tucker necessary conditions for efficiency to mathematical programs in normed linear spaces involving inequality, equality and set constraints with positive Lagrange multipliers of all the components of objective functions.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331930701761433