A convergent secant method for constrained optimization

Abstract

In this paper we combine a secant method with a trust region strategy so that the resulting algorithm not only has a local two-step superlinear rate, but also globally converges to Karush-Kuhn-Tucker points. The condition for proving these convergence properties is weaker than some trust region methods which use reduced Hessian asa tool. A minor revision of this algorithm is shown to possess a one-step superlinear rate.