Modified procedures of iterative prox-regularization (Q1975095)

Two algorithms for solving convex programming problems are suggested. The algorithms are based on the introduction of the prox-regularization into the scheme of the penalty function method. In contrast to conventional approaches, the number of steps in the analyzed algorithms of the prox-method is not fixed in advance for every penalty function and is determined in the process of the algorithm operation. For well known linearization method and penalty function method the corresponding minimizing sequences have been proved to converge to a solution of optimization problem under an appropriate choice of control parameters and certain additional assumptions.