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Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas

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Abstract

The aim of the present work is to use a metric intersection formula to estimate the subdifferential of the marginal function in the convex setting. This intersection formula includes many interesting situations in parametric convex programming, including the polyhedral one. It is expressed in terms of the objective function and the constrained multivalued mapping which govern the parametric program.

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Acknowledgements

The research of Duong Thi Viet An was partially supported by Thai Nguyen University of Sciences, Vietnam. The research of Abderrahim Jourani was partially supported by the EIPHI Graduate School (contract ANR-17-EURE-0002). The authors would like to thank the two anonymous referees and the handling Associate Editor for their very careful readings and valuable suggestions which have helped to greatly improve the presentation.

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Authors and Affiliations

  1. School of Management, Hangzhou Dianzi University, Hangzhou, 310018, China

    Duong Thi Viet An

  2. Department of Mathematics and Informatics, Thai Nguyen University of Sciences, Thai Nguyen City, Vietnam

    Duong Thi Viet An

  3. Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université de Bourgogne Franche-Comté, Dijon Cedex, France

    Abderrahim Jourani

Authors
  1. Duong Thi Viet An
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  2. Abderrahim Jourani
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Correspondence to Duong Thi Viet An.

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Communicated by Jen-Chih Yao.

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An, D.T.V., Jourani, A. Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas. J Optim Theory Appl 192, 82–96 (2022). https://doi.org/10.1007/s10957-021-01952-6

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  • DOI: https://doi.org/10.1007/s10957-021-01952-6

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