A feasible direction subgradient algorithm for a class of nondifferentiable optimization problems

Abstract

We present an implementable feasible direction subgradient algorithm for minimizing the maximum of a finite collection of functions subject to constraints. It is assumed that each function involved in defining the objective function is the sum of a finite collection of basic convex functions and that the number of different subgradient sets associated with nondifferentiable points of each basic function is finite on any bounded set. It is demonstrated that under certain conditions, including continuous differentiability of the constraints and a regularity condition of the µ feasible region, that the algorithm generates a feasible sequence which converges to an ε-optimal solution. Computational results for some example problems are included.