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A derivative-free descent method in set optimization

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Abstract

Based on a vectorization result in set optimization with respect to the set less order relation, this paper shows how to relate two nonempty sets on a computer. This result is developed for generalized convex sets and polyhedral sets in finite dimensional spaces. Using this approach a numerical method for the determination of optimal scenarios is presented. A new derivative-free descent method for the solution of set optimization problems is given together with numerical results in low dimensions.

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Acknowledgments

The author thanks the referees for helpful suggestions and comments and A. Löhne for his advice on Theorem 2.2 and a remark on Proposition 3.1.

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  1. Department Mathematik, Universität Erlangen-Nürnberg, Cauerstr. 11, D-91058 , Erlangen, Germany

    Johannes Jahn

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  1. Johannes Jahn
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Correspondence to Johannes Jahn.

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Jahn, J. A derivative-free descent method in set optimization. Comput Optim Appl 60, 393–411 (2015). https://doi.org/10.1007/s10589-014-9674-8

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  • DOI: https://doi.org/10.1007/s10589-014-9674-8

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