A direct search conjugate directions algorithm for unconstrained minimization

Abstract

A direct search algorithm for unconstrained minimization of smooth functions is described. The algorithm minimizes the function over a sequence of successively finer grids. Each grid is defined by a set of basis vectors. From time to time these basis vectors are updated to include available second derivative information by making some basis vectors mutually conjugate. Convergence to one or more stationary points is shown, and the finite termination property of conjugate direction methods on strictly convex quadratics is retained. Numerical results show that the algorithm is effective on a variety of problems including ill-conditioned problems.