On the Geometry Phase in Model-Based Algorithms for Derivative-Free Optimization

Giovanni Fasano(fasanounive.it)
Jose Luis Morales(nocedaleecs.northwestern.edu)
Jorge Nocedal(nocedaleecs.northwestern.edu)

Abstract: A numerical study of model-based methods for derivative-free optimization is presented. These methods typically include a geometry phase whose goal is to ensure the adequacy of the interpolation set. The paper studies the performance of an algorithm that dispenses with the geometry phase altogether (and therefore does not attempt to control the position of the interpolation set). Data is presented describing the evolution of the condition number of the interpolation matrix and the accuracy of the gradient estimate. The experiments are performed on smooth unconstrained optimization problems with dimensions ranging between 2 and 15.

Keywords: derivative-free optimization, nonlinear optimization

Category 1: Nonlinear Optimization

Citation: Tech Report, March 2009, Optimization Center, Northwestern University

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Entry Submitted: 03/14/2008
Entry Accepted: 03/14/2008
Entry Last Modified: 03/14/2008

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