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Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets

Author

Listed:
  • Duong Thi Viet An

    (Thai Nguyen University of Sciences)

  • Jen-Chih Yao

    (China Medical University)

Abstract

This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for $$\varepsilon $$ ε -subdifferentials, we obtain exact formulas for computing the $$\varepsilon $$ ε -subdifferential of the optimal value function. Several illustrative examples are also given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:1:d:10.1007_s10957-018-1431-1
    DOI: 10.1007/s10957-018-1431-1
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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. Alberto Seeger, 1996. "Subgradients of Optimal-Value Functions in Dynamic Programming: The Case of Convex Systems Without Optimal Paths," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 555-575, August.
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