Generalized Gradients and Paths of Descent
Jay S. Treiman · Optimization · 1986
There have been several algorithms in the literature that use Clabke's generalized gradients to find descent directions for minimizing Lipschitz functions, The result used to find these directions states that if zero is not a generalized gradient to a Lipschitz function f at xthen there is an y that is a direction of descent for f at all points in a neighborhood of x. In this paper it is shown that, even though there may not be descent directions, there are paths of descent if f is lower semicontinuous. This is done using a characterization of Clabke'S tangent cone in terms of Lipschitz paths.