COUPLING THE PROXIMAL POINT ALGORITHM WITH APPROXIMATION METHODS

We study the convergence of a diagonal process for minimizing a closed proper convex function f, in which a proximal point iteration is appl ied to a sequence of functions approximating f. We prove that, when th e approximation is sufficiently fast, and also when it is sufficiently slow, the sequence generated by the method converges toward a minimiz er of f. Comparison to previous work is provided through examples in p enalty methods for linear programming and Tikhonov regularization.