Multiobjective DC programs with infinite convex constraints

Authors:
Shaojian Qu;Mark Goh;Soon-Yi Wu;Robert Souza
Affiliations:
Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin, People's Republic of China 150080 and The Logistics Institute-Asia Pacific, National University of Si ...;The Logistics Institute-Asia Pacific, National University of Singapore, Singapore, Singapore;Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan and National Center for Theoretical Sciences, Tainan, Taiwan;The Logistics Institute-Asia Pacific, National University of Singapore, Singapore, Singapore
Venue:
Journal of Global Optimization
Year:
2014

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Abstract

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.