A quasisecant method for minimizing nonsmooth functions

Abstract

We present an algorithm to locally minimize nonsmooth, nonconvex functions. In order to find descent directions, the notion of quasisecants, introduced in this paper, is applied. We prove that the algorithm converges to Clarke stationary points. Numerical results are presented demonstrating the applicability of the proposed algorithm to a 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

AMS Subject Classification :

• 65K05
• 90C25

Acknowledgements

Dr. Adil Bagirov is the recipient of an Australian Research Council Australian Research Fellowship (Project number: DP 0666061).

We wish to thank an anonymous referee for comments that improved the quality of the paper.