Subdifferential calculus using \(\varepsilon\)-subdifferentials (Q1310821)

The authors establish a formula for the subdifferential \(\partial(f+ g)(x)\) of a sum of two convex functions \(f\) and \(g\), without assuming any constraint qualification hypothesis. They also consider the case of the composition of \(f\) with an affine mapping. Finally, they obtain a formula for the subdifferential of the infimal convolution of two convex functions, without assuming that the infimal convolution is attained. The general case of a marginal function associated to a convex program without optimal solutions has been previously studied by \textit{M. Moussaoui} and the reviewer [`Sensitivity analysis of optimal-value functions of convex parametric programs with possible empty solution sets', Preprint, March 1992, Univ. of Avignon, France; to appear in SIAM J. Optimization].