On the geometry phase in model-based algorithms for derivative-free optimization

Authors:
Giovanni Fasano;Jose Luis Morales;Jorge Nocedal
Affiliations:
Dipartimento di Matematica Applicata, Universita`'Foscari di Venezia and INSEAN, Venezia, Italy;Departamento de Matematicas, Instituto Tecnologico Autonomo de Mexico, Mexico, Mexico;Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, USA
Venue:
Optimization Methods & Software
Year:
2009

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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 are 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.