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On quasi \(\epsilon \)-solution for robust convex optimization problems

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Abstract

This paper devotes to the quasi \(\epsilon \)-solution (one sort of approximate solutions) for a robust convex optimization problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we establish approximate optimality theorem and approximate duality theorems in term of Wolfe type on quasi \(\epsilon \)-solution for the robust convex optimization problem. Moreover, some examples are given to illustrate the obtained results.

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Acknowledgments

The authors would like to express their sincere thanks to anonymous referees for variable suggestions and comments for the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Pukyong National University, Busan, 48513, Korea

    Jae Hyoung Lee & Liguo Jiao

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

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Lee, J.H., Jiao, L. On quasi \(\epsilon \)-solution for robust convex optimization problems. Optim Lett 11, 1609–1622 (2017). https://doi.org/10.1007/s11590-016-1067-8

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  • DOI: https://doi.org/10.1007/s11590-016-1067-8

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