Iterative regularization of a penalty method for an infinite-dimensional saddle-point search problem

In order to locate the minimax of a convex-concave functional in Hilbert space (or in a space continuously embedded in Hilbert space), subject to convex constraints, an iterative regularization of the integral penalty method is proposed for an iterative finite-dimensional approximation. A numerical algorithm is constructed by combining the proposed scheme with a stochastic quasigradient projection method. Convergence theorems are proved.