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On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization

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Abstract

We present approximate solutions for the robust semi-infinite multi-objective convex symmetric cone programming problem. By using the robust optimization approach, we establish an approximate optimality theorem and approximate duality theorems for approximate solutions in convex symmetric cone optimization problem involving infinitely many constraints to be satisfied and multiple objectives to be optimized simultaneously under the robust characteristic cone constraint qualification. We also give an example to illustrate the obtained results in an important special case, namely the robust semi-infinite multi-objective convex second-order cone program.

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Acknowledgements

The authors thank Yifan Dou from the Ohio State University for reading the manuscript and pointing out misprints. The authors also thank the two anonymous expert referees for their valuable suggestions from which the paper has benefited.

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Authors and Affiliations

  1. Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

    Baha Alzalg & Amira Achouak Oulha

  2. Department of Computer Science and Engineering, The Ohio State University, Columbus, OH, 43210, USA

    Baha Alzalg

  3. Department of Mathematics, University of Bachir El Ibrahimi, 34000, Bordj Bou Arreridj, Algeria

    Amira Achouak Oulha

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  1. Baha Alzalg
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  2. Amira Achouak Oulha
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Correspondence to Baha Alzalg.

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Alzalg, B., Oulha, A.A. On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization. Positivity 26, 86 (2022). https://doi.org/10.1007/s11117-022-00952-8

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