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On the Quantitative Solution Stability of Parameterized Set-Valued Inclusions

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Abstract

The subject of the present paper are stability properties of the solution set to set-valued inclusions. The latter are problems emerging in robust optimization and mathematical economics, which can not be cast in traditional generalized equations. The analysis here reported focuses on several quantitative forms of semicontinuity for set-valued mappings, widely investigated in variational analysis, which include, among others, calmness. Sufficient conditions for the occurrence of these properties in the case of the solution mapping to a parameterized set-valued inclusion are established. Consequences on the calmness of the optimal value function, in the context of parametric optimization, are explored. Some specific tools for the analysis of the sufficient conditions, in the case of set-valued inclusion with concave multifunction term, are provided in a Banach space setting.

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Acknowledgments

The author would like to express his gratitude to two anonymous referees for relevant remarks and useful suggestions, which helped him to improve the quality of the paper.

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  1. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via R. Cozzi, 55 - 20125, Milano, Italy

    A. Uderzo

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Uderzo, A. On the Quantitative Solution Stability of Parameterized Set-Valued Inclusions. Set-Valued Var. Anal 29, 425–451 (2021). https://doi.org/10.1007/s11228-020-00571-z

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