Abstract
We show that well-posedness (namely approximative well-posedness) properties of optimization problems are very efficient tools in subdifferential calculus of optimal value (marginal) function and in particular of infimal convolution. Under well-posedness conditions we establish an inclusion for the Mordukhovich limiting subdifferential of the marginal function and obtain new properties and descriptions of the Fréchet, proximal and Mordukhovich limiting subdifferentials of the infimal convolution. We also formulate sufficient conditions for well-posedness properties under consideration.
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The authors are grateful to the referee and the editor for very useful comments.
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The research of G.E. Ivanov is supported by the Russian Foundation for Basic Research, grant 18-01-00209.
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Ivanov, G.E., Thibault, L. Well-posedness and Subdifferentials of Optimal Value and Infimal Convolution. Set-Valued Var. Anal 27, 841–861 (2019). https://doi.org/10.1007/s11228-018-0493-4
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DOI: https://doi.org/10.1007/s11228-018-0493-4
Keywords
- Marginal function
- Optimal value function
- Infimal convolution
- Well-posedness
- Fréchet subdifferential
- Mordukhovich subdifferential
- Ekeland variational principle