Global Convergence of a Class of Trust Region Algorithms for Optimization with Simple Bounds

Abstract

This paper extends the known excellent global convergence properties of trust region algorithms for unconstrained optimization to the case where bounds on the variables are present. Weak conditions on the accuracy of the Hessian approximations are considered. It is also shown that, when the strict complementarily condition holds, the proposed algorithms reduce to an unconstrained calculation after finitely many iterations, allowing a fast asymptotic rate of convergence.