A quasisecant method for minimizing nonsmooth functions

In this paper a new algorithm to locally minimize nonsmooth, nonconvex functions is developed. We introduce the notion of secants and quasisecants for nonsmooth functions. The quasisecants are applied to find descent directions of locally Lipschitz functions. We design a minimization algorithm which uses quasisecants to find descent directions. We prove that this algorithm converges to Clarke stationary points. Numerical results are presented demonstrating the applicability of the proposed algorithm in wide variety of nonsmooth, nonconvex optimization problems. We also, compare the proposed algorithm with the bundle method using numerical results.