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Set-Valued and Variational Analysis

, Volume 27, Issue 4, pp 841–861 | Cite as

Well-posedness and Subdifferentials of Optimal Value and Infimal Convolution

  • Grigorii E. IvanovEmail author
  • Lionel Thibault
Article

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.

Keywords

Marginal function Optimal value function Infimal convolution Well-posedness Fréchet subdifferential Mordukhovich subdifferential Ekeland variational principle 

Mathematics Subject Classification (2010)

49J52 46N10 

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Notes

Acknowledgments

The authors are grateful to the referee and the editor for very useful comments.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  2. 2.Institut Montpelliérain Alexander GrothendieckUniversité de MontpellierMontpellier Cedex 05France
  3. 3.Centro de Modelamiento MatematicoUniversidad de ChileSantiagoChile

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