Steepest Descent for Optimization Problems with Nondifferentiable Cost Functionals,

The steepest descent method is a commonly used algorithm for finding the minimum of a differentiable cost functional. At each iteration a descent is made at the direction of the negative gradient according to some step size selection scheme. This paper has two objectives. First to examine the natural extension of the steepest descent algorithm for minimizing a directionally differentiable function mapping R sup n into the real line. Second, the paper is to propose a new descent algorithm for minimizing an extended real valued convex function. Author