Minimizing and Stationary Sequences of Convex Constrained Minimization Problems

In the asymptotic analysis of the minimization problem for a nonsmooth convex function on a closed convex set X in ⁿ, one can consider the corresponding problem of minimizing a smooth convex function F on ⁿ, where F denotes the Moreau–Yosida regularization of f. We study the interrelationship between the minimizing/stationary sequence for f and that for F. An algorithm is given to generate iteratively a possibly unbounded sequence, which is shown to be a minimizing sequence of f under certain regularity and uniform continuity assumptions.