A Combined Variable Metric - Conjugate Gradient Algorithm for a Class of Large Scale Unconstrained Minimization Problems

An algorithm is being presented for a special class of unconstrained minimization problems. The algorithm exploits the special structure of the Hessian in the problems under consideration, It is based on applying Bertsekas' I-1] Scaled Partial Conjugate Gradient method with respect to a metric that is updated by the Rank One update, using gradients obtained in the preceeding steps. Two classes of problems are-presented having the structure assumed in designing the proposed algorithm. In both cases the algorithm uses only first derivative information. Furthermore, it possesses quadratic termination in considerably fewer steps than the number of variables.