Directional Lipschitzian optimal solution of infinite-dimensional optimization problems

This paper presents a study of the Lipschitz dependence of the optimal solution of elementary convex programs in a Hilbert space when the equality constraints are subjected to small perturbations in some fixed direction and with the sub- and super-quadratic growth conditions. This study follows the recent results of Janin and Gauvin [1] related to the finite-dimentional case. As an illustrative example, we study the directional derivative with respect to the boundary conditions of the infimum (value function) of the Mossolov problem in space dimension one.