2018/05/04 by An, Duong Thi Viet, Yao, Jen-Chih
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1805.01656
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 ε-subdifferentials, we obtain exact formulas for computing the ε-subdifferential of the optimal value function. Several illustrative examples are also given.