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On \(\epsilon \)-solutions for robust semi-infinite optimization problems

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Abstract

In this paper, we consider semi-infinite optimization problems involving a convex objective function and infinitely many convex constraint functions with data uncertainty, and give its robust counterpart \(\mathrm{(RSIP)}\). Moreover, we consider approximate solutions (\(\epsilon \)-solutions) for \(\mathrm{(RSIP)}\). Using robust optimization approach (worst-case approach), we establish robust necessary optimality and robust sufficient theorems and give duality results for \(\epsilon \)-solutions for \(\mathrm{(RSIP)}\) under a closed convex cone constraint qualification. Moreover, an example is given to illustrate the obtained duality results.

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Acknowledgements

The authors would like to express their sincere thanks to anonymous referee for their very helpful and valuable suggestions and comments for the paper.

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Correspondence to Gue Myung Lee.

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

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Lee, J.H., Lee, G.M. On \(\epsilon \)-solutions for robust semi-infinite optimization problems. Positivity 23, 651–669 (2019). https://doi.org/10.1007/s11117-018-0630-1

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