A modified version of the Powell's method for derivative free optimization

MARÍA B. AROUXÉT; NÉLIDA ECHEBEST; ELVIO A. PILOTTA

Campinas, SP, Brasil

Workshop; VII Brazilian Workshop on Continuous Optimization; 2008

Universidad Estadual de Campinas, IMPA, FAPESP

Derivative free optimization methods, like Powell´s NEWUOA algorithm, are designed for solving nonlinear optimization problem where the derivatives  of the objective function are not available. Formally, we consider the problem of minimize a smooth nonlinear  objective function without constraints. NEWUOA is essentially a combination of a trust region framework with quadratic interpolation of the objective function. A modification of this method is proposed based on the spectral projected gradient method (SPG). The last one is an algorithm developed for large-scale convex-constrained mathematical programming problems. It is very useful when projections on the feasible set are easy to compute. Numerical experiments using a set of test problems are presented.