Abstract
As a complement to a recent paper by An and Yen (Appl Anal 94:108---128, 2015) on subdifferentials of the optimal value function in parametric convex programming under inclusion constraints and functional constraints, this paper studies the differential stability of convex optimization problems under a regularity condition of Aubin's type (Aubin in Optima and equilibria: an introduction to nonlinear analysis. Springer, New York, 1998). By a suitable sum rule for convex subdifferentials, we obtain exact formulas for the subdifferential and singular subdifferential of the optimal value function. Illustrative examples and a detailed comparison of our results with those of the above-mentioned paper are given.
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