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Multiobjective DC programs with infinite convex constraints

Author

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  • Shaojian Qu
  • Mark Goh
  • Soon-Yi Wu
  • Robert Souza

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Shaojian Qu & Mark Goh & Soon-Yi Wu & Robert Souza, 2014. "Multiobjective DC programs with infinite convex constraints," Journal of Global Optimization, Springer, vol. 59(1), pages 41-58, May.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:1:p:41-58
    DOI: 10.1007/s10898-013-0091-9
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    References listed on IDEAS

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    1. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    2. C.F. Wen & S.Y. Wu, 2004. "Duality theorems and algorithms for linear programming in measure spaces," Journal of Global Optimization, Springer, vol. 30(2), pages 207-233, November.
    3. N. J. Huang & J. Li & S. Y. Wu, 2009. "Optimality Conditions for Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 323-342, August.
    4. V. Jeyakumar, 1997. "Asymptotic Dual Conditions Characterizing Optimality for Infinite Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 153-165, April.
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    Cited by:

    1. Outi Montonen & Kaisa Joki, 2018. "Bundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraints," Journal of Global Optimization, Springer, vol. 72(3), pages 403-429, November.

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