A Steepest Gradient Method with Nonmonotone Adaptive Step-sizes for the Nonconvex Minimax and Multi-Objective Optimization Problems
Abstract
This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and pseudoconvex differentiate component functions. The proposed method is applied using a referenced-based approach to solve the nonconvex multiobjective programming problems. The convergence to weakly efficient or Pareto stationary solutions is proved for pseudoconvex or quasiconvex multiobjective optimization problems, respectively. A variety of numerical experiments are provided for each scenario to verify the correctness of the theoretical results corresponding to the algorithms proposed for the minimax and multiobjective optimization problems.
Cite
@article{arxiv.2502.02010,
title = {A Steepest Gradient Method with Nonmonotone Adaptive Step-sizes for the Nonconvex Minimax and Multi-Objective Optimization Problems},
author = {Nguyen Duc Anh and Tran Ngoc Thang},
journal= {arXiv preprint arXiv:2502.02010},
year = {2025}
}
Comments
20 pages