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Proximal Point Algorithms for Multi-criteria Optimization with the Difference of Convex Objective Functions

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Abstract

This paper focuses on solving a class of multi-criteria optimization with the difference of convex objective functions. Proximal point algorithms, extensively studied for scalar optimization, are extended to our setting. We show that the proposed algorithms are well posed and globally convergent to a critical point. For an application, the new methods are used to a multi-criteria model arising in portfolio optimization. The numerical results show the efficiency of our methods.

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Acknowledgments

The authors thank two anonymous referees for their insightful comments that improved the paper in numerous ways. This work was supported by the National Natural Science Foundation of China (Nos. 71201040, 11201099, 71571055), and A*STAR SERC Grant (No. 1224200003).

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Authors and Affiliations

  1. Business School, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai, 200093, China

    Ying Ji

  2. Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin, China

    Ying Ji

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

    Ying Ji, Mark Goh & Robert de Souza

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

    Mark Goh

Authors
  1. Ying Ji
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  2. Mark Goh
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  3. Robert de Souza
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Correspondence to Ying Ji.

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Ji, Y., Goh, M. & de Souza, R. Proximal Point Algorithms for Multi-criteria Optimization with the Difference of Convex Objective Functions. J Optim Theory Appl 169, 280–289 (2016). https://doi.org/10.1007/s10957-015-0847-0

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  • DOI: https://doi.org/10.1007/s10957-015-0847-0

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