Variable Metric Method for Unconstrained Multiobjective Optimization Problems
Optimization and Control
2022-07-18 v1
Abstract
In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved that accumulation points of the sequence are Pareto critical points. Then, without convexity assumption, strong convergence is established for the proposed method. Moreover, we use a common matrix to approximate the Hessian matrices of all objective functions, along which, a new nonmonotone line search technique is proposed to achieve a local superlinear convergence rate. Finally, several numerical results demonstrate the effectiveness of the proposed method.
Cite
@article{arxiv.2207.07286,
title = {Variable Metric Method for Unconstrained Multiobjective Optimization Problems},
author = {Jian Chen and Gaoxi Li and Xinmin Yang},
journal= {arXiv preprint arXiv:2207.07286},
year = {2022}
}