A derivative-free method for linearly constrained nonsmooth optimization

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July 2006, 2(3): 319-338. doi: 10.3934/jimo.2006.2.319

A derivative-free method for linearly constrained nonsmooth optimization

A. M. Bagirov ^1, , Moumita Ghosh ^1, and Dean Webb ^1,

1.	Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, 3353, Australia, Australia, Australia

Received December 2005 Revised April 2006 Published July 2006

Abstract
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This paper develops a new derivative-free method for solving linearly constrained nonsmooth optimization problems. The objective functions in these problems are, in general, non-regular locally Lipschitz continuous function. The computation of generalized subgradients of such functions is difficult task. In this paper we suggest an algorithm for the computation of subgradients of a broad class of non-regular locally continuous Lipschitz functions. This algorithm is based on the notion of a discrete gradient. An algorithm for solving linearly constrained nonsmooth optimization problems based on discrete gradients is developed. We report preliminary results of numerical experiments. These results demonstrate that the proposed algorithm is efficient for solving linearly constrained nonsmooth optimization problems.

Keywords: discrete gradient., Nonsmooth optimization, constrained optimization, subdifferential, non-regular functions.

Mathematics Subject Classification: Primary: 65K05; Secondary:90C2.

Citation: A. M. Bagirov, Moumita Ghosh, Dean Webb. A derivative-free method for linearly constrained nonsmooth optimization. Journal of Industrial & Management Optimization, 2006, 2 (3) : 319-338. doi: 10.3934/jimo.2006.2.319

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