A Reeective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables 1

We propose a new algorithm, a reeective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. The method applies to a general (indeenite) quadratic function, for which a local minimizer subject to bounds is required, and is particularily suitable for the large-scale problem. Our new method exhibits strong convergence properties, global and quadratic convergence, and appears to have signiicant practical potential. Strictly feasible points are generated. Experimental results on moderately large and sparse problems support the claim of practicality for large-scale problems. 1. Introduction. In this paper we propose a new algorithm for solving the box