  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.
