A Retrospective Cubic Regularization for Unconstrained Optimization Using Nonmonotone Techniques 

Yajing Wang, Qinghua Zhou*

College of Mathematics and Information Science, Hebei University, Baoding, 071002, China

Abstract: In recent years, cubic regularization algorithm for unconstrained optimization has been defined as alternative to trust-region and line search schemes. These regularization techniques are based on the strategy of computing an approximate global minimizer of a cubic overestimator of the objective function. It can ef-fectively handle with some worst cases and improve the iteration complexity. In this work, we investigate a new approach which combines retrospective adaptive cubic regularization algorithm and some nonmonotone linesearch strategy. Under some standard assumptions, the global convergence properties are given.

Keywords: Unconstrained optimization; Cubic regularization; Retrospective trust region method; Global convergence