Some Recent Progress In Unconstrained Nonlinear Optimization

摘要

In this paper, we present some recent progress in numerical optimization methods for solving unconstrained optimization problems. This paper is organized around three main classes of algorithms for unconstrained optimization: conjugate gradient, quasi-Newton and trust region methods. By using the sufficient descent property, we propose some new conjugate gradient methods. Then, we describe some work modifying the original quasi-Newton equation to give new updates, based on which, we present four new quasi-Newton methods. In the context of a trust region framework, we focus on techniques which ensure that the considered model is always a strictly convex quadratic model. We finally conclude the paper with a discussion of perspectives for these methods.