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Further Results on Differential Stability of Convex Optimization Problems

Author

Listed:
  • Duong Thi Viet An

    (Thai Nguyen University
    National Sun Yat-Sen University)

  • Jen-Chih Yao

    (China Medical University
    China Medical University Hospital)

Abstract

As a complement to a recent paper by An and Yen (Appl Anal 94:108–128, 2015) on subdifferentials of the optimal value function in parametric convex programming under inclusion constraints and functional constraints, this paper studies the differential stability of convex optimization problems under a regularity condition of Aubin’s type (Aubin in Optima and equilibria: an introduction to nonlinear analysis. Springer, New York, 1998). By a suitable sum rule for convex subdifferentials, we obtain exact formulas for the subdifferential and singular subdifferential of the optimal value function. Illustrative examples and a detailed comparison of our results with those of the above-mentioned paper are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-016-0900-7
    DOI: 10.1007/s10957-016-0900-7
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    References listed on IDEAS

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    1. Bernhard Gollan, 1984. "On The Marginal Function in Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 208-221, May.
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    Cited by:

    1. Duong Thi Viet An & Jen-Chih Yao, 2019. "Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 126-143, April.
    2. 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.

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