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

Author

Listed:
  • Duong Thi Viet An

    (Hangzhou Dianzi University
    Thai Nguyen University of Sciences)

  • Abderrahim Jourani

    (Université de Bourgogne Franche-Comté)

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.

Suggested Citation

  • Duong Thi Viet An & Abderrahim Jourani, 2022. "Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 82-96, January.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:1:d:10.1007_s10957-021-01952-6
    DOI: 10.1007/s10957-021-01952-6
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    References listed on IDEAS

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    1. Duong Thi Viet An & Jen-Chih Yao, 2016. "Further Results on Differential Stability of Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 28-42, July.
    2. Bernhard Gollan, 1984. "On The Marginal Function in Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 208-221, May.
    3. Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
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