Optimality conditions and duality in nonsmooth multiobjective optimization problems

Exploiting some tools of modern variational analysis involving the approximate extremal principle, the fuzzy sum rule for the Fréchet subdifferential, the sum rule for the limiting subdifferential and the scalarization formulae of the coderivatives, we establish necessary conditions for (weakly) eff...

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Vydané v:Annals of operations research Ročník 217; číslo 1; s. 117 - 136
Hlavní autori: Chuong, Thai Doan, Kim, Do Sang
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.06.2014
Springer
Springer Nature B.V
Predmet:
Approximation
Business and Management
Combinatorics
Constraining
Differential equations
Fuzzy
Fuzzy logic
Fuzzy set theory
Inequalities
Inequalities (Mathematics)
Mathematical functions
Mathematical optimization
Mathematical research
Operations research
Operations Research/Decision Theory
Optimization
Studies
Sum rules
Theory of Computation
49K99
Limiting subdifferential
90C46
Multiobjective optimization
Optimality condition
65K10
90C29
Duality
invex-infine function
The (KKT) condition
ISSN:0254-5330, 1572-9338
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Popis
Shrnutí:Exploiting some tools of modern variational analysis involving the approximate extremal principle, the fuzzy sum rule for the Fréchet subdifferential, the sum rule for the limiting subdifferential and the scalarization formulae of the coderivatives, we establish necessary conditions for (weakly) efficient solutions of a multiobjective optimization problem with inequality and equality constraints. Sufficient conditions for (weakly) efficient solutions of an aforesaid problem are also provided by means of employing L -(strictly) invex-infine functions defined in terms of the limiting subdifferential. In addition, we introduce types of Wolfe and Mond–Weir dual problems and investigate weak/strong duality relations.
Bibliografia:SourceType-Scholarly Journals-1
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-014-1552-3