Multiobjective DC programs with infinite convex constraints

New results are established for multiobjective DC programs with infinite convex constraints (MOPIC) that are defined on Banach spaces (finite or infinite dimensional) with objectives given as the difference of convex functions. This class of problems can also be called multiobjective DC semi-infinit...

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Vydáno v:Journal of global optimization Ročník 59; číslo 1; s. 41 - 58
Hlavní autoři: Qu, Shaojian, Goh, Mark, Wu, Soon-Yi, De Souza, Robert
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.05.2014
Springer
Springer Nature B.V
Témata:
Banach space
Banach spaces
Computational mathematics
Computer Science
Convex analysis
Direct current
Duality theorem
Euclidean space
Investment analysis
Joints
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Pareto efficiency
Pareto optimality
Pareto optimum
Real Functions
Studies
Duality
(weak) Pareto efficiency
Optimality
Saddle point
Multiobjective DC programs with infinite convex constraints
ISSN:0925-5001, 1573-2916
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Popis
Shrnutí:New results are established for multiobjective DC programs with infinite convex constraints (MOPIC) that are defined on Banach spaces (finite or infinite dimensional) with objectives given as the difference of convex functions. This class of problems can also be called multiobjective DC semi-infinite and infinite programs, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Such problems have not been studied as yet. Necessary and sufficient optimality conditions for the weak Pareto efficiency are introduced. Further, we seek a connection between multiobjective linear infinite programs and MOPIC. Both Wolfe and Mond-Weir dual problems are presented, and corresponding weak, strong, and strict converse duality theorems are derived for these two problems respectively. We also extend above results to multiobjective fractional DC programs with infinite convex constraints. The results obtained are new in both semi-infinite and infinite frameworks.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-013-0091-9