Nonsmooth local optimization via direct search

Abstract A direct search method for local unconstrained optimization of nonsmooth functions is presented. The method performs forward tracking line searches along a sequence of poll directions, where the lengths of many poll directions are bounded away from zero. Convergence is shown under mild conditions when the poll directions are generated from any scrambled Halton sequence. An arbitrary step is incorporated into the method, allowing other line searches to be used to accelerate the convergence rate. This paper compares the performance of the Sobol, standard Halton and a scrambled Halton poll sequences with no arbitrary step. Numerical trials show the latter performs similarly to the Sobol sequence and outperforms the standard Halton sequence.