American Institute of Mathematical Sciences

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April  2007, 3(2): 321-334. doi: 10.3934/jimo.2007.3.321

Survey of trust-region derivative free optimization methods

Bülent Karasözen 1,

1. 

Middle East Technical University, Department of Mathematics & Institute of Applied Mathematics, 06531 Ankara, Turkey

Received  September 2006 Revised  January 2007 Published  April 2007

In this survey article we give the basic description of the interpolation based derivative free optimization methods and their variants. We review the recent contributions dealing with maintaining the geometry of the interpolation set, the management of the trust region radius and the stopping criteria. Derivative free algorithms developed for problems with some structure, like for partially separable functions, are discussed. Two different versions of derivative free algorithms are applied for the optimization of the configuration of the geometry of a stirrer. Numerical results are presented to show the applicability of the algorithms to practical problems.
Keywords: multi-variate interpolation, derivative-free optimization, partially separable functions., trust-region methods.
Mathematics Subject Classification: Primary: 90C56 ; Secondary: 65D0.
Citation: Bülent Karasözen. Survey of trust-region derivative free optimization methods. Journal of Industrial & Management Optimization, 2007, 3 (2) : 321-334. doi: 10.3934/jimo.2007.3.321
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