A quasisecant method for minimizing nonsmooth functions

Adil Bagirov(a.bagirovballarat.edu.au)
Asef Nazari Ganjehlou(a.nazariballarat.edu.au)

Abstract: 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.

Keywords: nonsmooth optimization, nonconvex optimization, subdifferential, bundle method.

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization

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Entry Submitted: 03/09/2009
Entry Accepted: 03/10/2009
Entry Last Modified: 03/09/2009

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