An Approximate Penalty Method with Descent for Convex Optimization Problems

Abstract

We propose a penalty method for general convex constrained optimization problems, where each auxiliary penalized problem is solved approximately with a special composite descent method. Direction finding choice in this method is found with the help of an equivalent equilibrium type problem. This allows one to keep the complete structure of the initial problem, although without nonlinear constraints and to simply calculate the descent direction in separable problems. Convergence of the method in primal and dual variables is established under rather weak assumptions.