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On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems

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Abstract

In this paper, we consider a semi-infinite multiobjective optimization problem with more than two differentiable objective functions and uncertain constraint functions, which is called a robust semi-infinite multiobjective optimization problem and give its robust counterpart \({\mathrm{(RSIMP)}}\) of the problem, which is regarded as the worst case of the uncertain semi-infinite multiobjective optimization problem. We prove a necessary optimality theorem for a weakly robust efficient solution of \({\mathrm{(RSIMP)}} \), and then give a sufficient optimality theorem for a weakly robust efficient solution of \({\mathrm{(RSIMP)}}\). We formulate a Wolfe type dual problem of \({\mathrm{(RSIMP)}}\) and give duality results which hold between \({\mathrm{(RSIMP)}}\) and its dual problem.

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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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Correspondence to Gue Myung Lee.

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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2005378).

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Lee, J.H., Lee, G.M. On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems. Ann Oper Res 269, 419–438 (2018). https://doi.org/10.1007/s10479-016-2363-5

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  • DOI: https://doi.org/10.1007/s10479-016-2363-5

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