The epsilon strategy in variational analysis : illustration with the closed convexitication of a function
Résumé
In this work, we concentrate our interest and efforts on general variational (or optimization) problems which do not have solutions necessarily, but which do have approximate solutions (or solutions within ε > 0). We shall see how to recover all the (exact) min-imizers of the relaxed version of the original problem (by closed-convexification of the objective function) in terms of the ε-minimizers of the original problem. Applications to two approximation problems in a Hilbert space setting will be shown.