This paper on "Solution of Large Scale Partially Separable Unconstrained Optimization Problems Using Element-by-Element Preconditioners" was presented at the NAFEMS World Congress on Design, Simulation & Optimisation: Reliability & Applicability of Computational Methods - 9-11 April 1997, Stuttgart, Germany.

Introduction to Paper

We study the numerical solution of large scale unconstrained optimization problems. We consider the minimization of a partially separable objective function f(x). Typically, this occurs when f_i(x) is only a function of a small subset of the variables x, but may, of course, happen for other reasons. The decomposition (1) is extremely general. Indeed, any sufficiently differentiable function with a sparse Hessian matrix may be expressed in this form [1]. In this paper, we shall be concerned with those partially separable functions.