Differential stability of convex optimization problems under weaker conditions

Differential stability properties of convex optimization problems in Hausdorff locally convex topological vector spaces are considered in this paper. We obtain new formulas for the subdifferential and the singular subdifferential of the optimal value function of convex optimization problems. Namely, instead of using the traditional Moreau-Rockafellar Theorem, we employ a sum rule for subdifferentials of two convex functions from the work of Correa, Hantoute, and Lopez [Weaker conditions for subdifferential calculus of convex functions. J Funct Anal. 2016;271:1177-1212]. Detailed comparisons with some known results are also given in this paper.