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Approximate Optimality and Approximate Duality for Quasi Approximate Solutions in Robust Convex Semidefinite Programs

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Abstract

In this paper, we study quasi approximate solutions for a convex semidefinite programming problem in the face of data uncertainty. Using the robust optimization approach (worst-case approach), approximate optimality conditions and approximate duality theorems for quasi approximate solutions in robust convex semidefinite programming problems are explored under the robust characteristic cone constraint qualification. Moreover, some examples are given to illustrate the obtained results.

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Acknowledgements

The second author was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIP) (NRF-2016R1A2B1006430). The authors would like to express their sincere thanks to both the handling editor and the anonymous referees, who have given several valuable and helpful suggestions and comments to improve the initial manuscript of the paper.

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  1. Department of Applied Mathematics, Pukyong National University, Busan, Republic of Korea

    Liguo Jiao & Jae Hyoung Lee

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  1. Liguo Jiao
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  2. Jae Hyoung Lee
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Correspondence to Jae Hyoung Lee.

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Communicated by Evgeni A. Nurminski.

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Jiao, L., Lee, J.H. Approximate Optimality and Approximate Duality for Quasi Approximate Solutions in Robust Convex Semidefinite Programs. J Optim Theory Appl 176, 74–93 (2018). https://doi.org/10.1007/s10957-017-1199-8

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  • DOI: https://doi.org/10.1007/s10957-017-1199-8

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