Differential stability of convex optimization problems with possibly empty solution sets
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 -subdifferentials, we obtain exact formulas for computing the -subdifferential of the optimal value function. Several illustrative examples are also given.
Cite
@article{arxiv.1805.01656,
title = {Differential stability of convex optimization problems with possibly empty solution sets},
author = {Duong Thi Viet An and Jen-Chih Yao},
journal= {arXiv preprint arXiv:1805.01656},
year = {2018}
}