# American Institute of Mathematical Sciences

April  2007, 3(2): 381-398. doi: 10.3934/jimo.2007.3.381

## An update rule and a convergence result for a penalty function method

 1 School of Mathematics and Statistics, University of South Australia, Mawson Lakes, S.A. 5095 Australia, and Centre for Informatics and Applied Optimization, University of Ballarat, Victoria, Australia 2 School of Mathematics and Statistics, University of South Australia, Mawson Lakes, S.A. 5095, Australia

Received  September 2006 Revised  January 2007 Published  April 2007

We use a primal-dual scheme to devise a new update rule for a penalty function method applicable to general optimization problems, including nonsmooth and nonconvex ones. The update rule we introduce uses dual information in a simple way. Numerical test problems show that our update rule has certain advantages over the classical one. We study the relationship between exact penalty parameters and dual solutions. Under the differentiability of the dual function at the least exact penalty parameter, we establish convergence of the minimizers of the sequential penalty functions to a solution of the original problem. Numerical experiments are then used to illustrate some of the theoretical results.
Citation: Regina S. Burachik, C. Yalçın Kaya. An update rule and a convergence result for a penalty function method. Journal of Industrial & Management Optimization, 2007, 3 (2) : 381-398. doi: 10.3934/jimo.2007.3.381
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