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arXiv · 1805.01656

Differential stability of convex optimization problems with possibly empty solution sets

Duong Thi Viet An·Jen-Chih Yao
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Abstract

As a complement to two recent papers by An and Yen [An, D.T.V., Yen, N.D.: Differential stability of convex optimization problems under inclusion constraints. Appl. Anal., 94, 108--128 (2015)], and by An and Yao [An, D.T.V., Yao, J.-C.: Further results on differential stability of convex optimization problems. J. Optim. Theory Appl., 170, 28--42 (2016)] on subdifferentials of the optimal value function of infinite-dimensional convex optimization problems, this paper studies the differential stability of convex optimization problems, where the solution set may be empty. By using a suitable sum rule for $\varepsilon$-subdifferentials, we obtain exact formulas for computing the $\varepsilon$-subdifferential of the optimal value function. Several illustrative examples are also given.

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Duong Thi Viet An, Jen-Chih Yao. 2018-05-04. Differential stability of convex optimization problems with possibly empty solution sets. https://arxiv.org/abs/1805.01656

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