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Multiobjective DC programs with infinite convex constraints

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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.

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Acknowledgments

The authors are very grateful to the editor in chief and the anonymous referee who have made many constructive comments that have helped to improve the presentation and results of the paper. This work was supported by Natural Scientific Foundation of China (Nos. 71201040, 11201099) and by Major Program of the National Natural Science Foundation of China (No. 71031003). This work was also supported by Postdoctoral Science-Research Development Foundation of Heilongjiang Province (No. LBH-Q11118) and by NOLFR-314-000-080-720.

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Authors and Affiliations

  1. Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Rm. 453, Bldg. 2H, 2 Yikuang Str., Nangang Dist., Harbin, 150080, People’s Republic of China

    Shaojian Qu

  2. The Logistics Institute-Asia Pacific, National University of Singapore, Singapore, Singapore

    Shaojian Qu, Mark Goh & Robert De Souza

  3. Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan

    Soon-Yi Wu

  4. National Center for Theoretical Sciences, Tainan, Taiwan

    Soon-Yi Wu

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  1. Shaojian Qu
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  2. Mark Goh
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  4. Robert De Souza
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Correspondence to Shaojian Qu.

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Qu, S., Goh, M., Wu, SY. et al. Multiobjective DC programs with infinite convex constraints. J Glob Optim 59, 41–58 (2014). https://doi.org/10.1007/s10898-013-0091-9

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  • DOI: https://doi.org/10.1007/s10898-013-0091-9

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