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On approximate solutions for robust convex semidefinite optimization problems

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Abstract

In this paper, we consider approximate solutions (\(\epsilon \)-solutions) for a convex semidefinite programming problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we prove an approximate optimality theorem and approximate duality theorems for \(\epsilon \)-solutions in robust convex semidefinite programming problem under the robust characteristic cone constraint qualification. Moreover, an example is given to illustrate the obtained results.

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Acknowledgements

This research was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIP) (NRF-2016R1A2B1006430).

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

    Jae Hyoung Lee & Gue Myung Lee

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  1. Jae Hyoung Lee
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  2. Gue Myung Lee
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Correspondence to Gue Myung Lee.

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Lee, J.H., Lee, G.M. On approximate solutions for robust convex semidefinite optimization problems. Positivity 22, 845–857 (2018). https://doi.org/10.1007/s11117-017-0549-y

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