A Descent Numerical Method for Optimization Problems with Nondifferentiable Cost Functionals

Abstract

In this paper we consider the numerical solution of convex optimization problems with nondifferentiable cost functionals. We propose a new algorithm, the $\varepsilon $-subradient method, a large step, double iterative algorithm which converges rapidly under very general assumptions. We discuss the application of the algorithm in some problems of nonlinear programming and optimal control and we show that the $\varepsilon $-subgradient method contains as a special case a minimax algorithm due to Pshenichnyi [5].