An alternative three-dimensional subspace method based on conic model for unconstrained optimization

¹ School of Mathematics and Information Science, Guangxi University, Nanning 530004, P.R. China
² Xiangsihu College of GuangXi University for Nationalities, Nanning 530000, P.R. China
³ College of Mathematics and Statistics, Nanning Normal University, Nanning 530001, P.R. China

^* Corresponding author: ysw@gxu.edu.cn

Received: 2 November 2022
Accepted: 3 October 2023

Abstract

In this paper, a three-dimensional subspace conjugate gradient method is proposed, in which the search direction is generated by minimizing the approximation model of the objective function in a three-dimensional subspace. The approximation model is not unique and is alternative between quadratic model and conic model by the specific criterions. The strategy of initial stepsize and nonmonotone line search are adopted, and the global convergence of the presented algorithm is established under mild assumptions. In numerical experiments, we use a collection of 80 unconstrained optimization test problems to show the competitive performance of the presented method.