A New Generating Set Search Algorithm for Partially Separable Functions

Abstract

A new derivative-free optimization method for unconstrained optimization of partially separable functions is presented. Using average curvature information computed from sampled function values the method generates an average Hessian-like matrix and uses its eigenvectors as new search directions. For partially separable functions, many of the entries of this matrix will be identically zero. The method is able to exploit this property and as a consequence update its search directions more often than if sparsity is not taken into account. Numerical results show that this is a more effective method for functions with a topography which requires frequent updating of search directions for rapid convergence. The method is an important extension of a method for nonseparable functions previously published by the authors. This new method allows for problems of larger dimension to be solved, and will in most cases be more efficient.