On duality for mathematical programs with vanishing constraints

In this paper, we formulate and study Wolfe and Mond–Weir type dual models for a difficult class of optimization problems known as the mathematical programs with vanishing constraints. We establish the weak, strong, converse, restricted converse and strict converse duality results under the assumpti...

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Published inAnnals of operations research Vol. 243; no. 1-2; pp. 249 - 272
Main Authors Mishra, S. K., Singh, Vinay, Laha, Vivek
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2016
Springer
Springer Nature B.V
Subjects
Algorithms
Business and Management
Combinatorics
Constraint modelling
Convexity
Duality theory (Mathematics)
Mathematical analysis
Mathematical models
Mathematical optimization
Mathematical research
Operations research
Operations Research/Decision Theory
Optimization
Theory of Computation
Mond–Weir dual
Duality results
Mathematical programs with vanishing constraints
Wolfe dual
Generalized convexity
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Summary:In this paper, we formulate and study Wolfe and Mond–Weir type dual models for a difficult class of optimization problems known as the mathematical programs with vanishing constraints. We establish the weak, strong, converse, restricted converse and strict converse duality results under the assumptions of convexity and strict convexity between the primal mathematical program with vanishing constraints and the corresponding Wolfe type dual. We also derive the weak, strong, converse, restricted converse and strict converse duality results between the primal mathematical program with vanishing constraints and the corresponding Mond–Weir type dual under the assumptions of pseudoconvex, strict pseudoconvex and quasiconvex functions.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-015-1814-8