A DESCENT METHOD WITH LINEAR-PROGRAMMING SUBPROBLEMS FOR NONDIFFERENTIABLE CONVEX-OPTIMIZATION

Most of the descent methods developed so far suffer from the computati onal burden due to a sequence of constrained quadratic subproblems whi ch are needed to obtain a descent direction. In this paper we present a class of proximal-type descent methods with a new direction-finding subproblem. Especially, two of them have a linear programming subprobl em instead of a quadratic subproblem. Computational experience of thes e two methods has been performed on two well-known test problems. The results show that these methods are another very promising approach fo r nondifferentiable convex optimization.