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Proximal Point Algorithms for Convex Multi-criteria Optimization with Applications to Supply Chain Risk Management

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Abstract

We study a class of convex multi-criteria optimization problems with convex objective functions under linear constraints. We use a non-scalarization method—namely, two implementable proximal point algorithms—to obtain the Pareto optimum under multi-criteria optimization. We show that the algorithms are globally convergent. We apply the algorithms to a supply chain risk management problem under multi-criteria considerations.

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Acknowledgments

The authors thank two anonymous referees for their insightful comments that improved the paper in numerous ways. The work is supported by a research grant from the Science and Engineering Research Council (SERC), A*STAR (Title of Supported Project: Master Facilitative Control Tower for Risk Management of Complex Supply Chains and Ref Number: 1121790043). This work is also supported by the Natural Scientific Foundation of China (Nos. 71201040, 11201099) and by Major Program of the National Natural Science Foundation of China (No. 71031003).

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Authors and Affiliations

  1. Harbin Institute of Technology, Rm.519, Bldg.2H, 2 Yikuang Str., Nangang Dist., Harbin, 150080, People’s Republic of China

    Shao-Jian Qu & Tie-Nan Wang

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

    Shao-Jian Qu, Mark Goh & Robert De Souza

  3. Business School, National University of Singapore, Singapore, Singapore

    Mark Goh

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  1. Shao-Jian Qu
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  2. Mark Goh
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  3. Robert De Souza
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  4. Tie-Nan Wang
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Correspondence to Shao-Jian Qu.

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Qu, SJ., Goh, M., De Souza, R. et al. Proximal Point Algorithms for Convex Multi-criteria Optimization with Applications to Supply Chain Risk Management. J Optim Theory Appl 163, 949–956 (2014). https://doi.org/10.1007/s10957-014-0540-8

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  • DOI: https://doi.org/10.1007/s10957-014-0540-8

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