Yushan Bai, Jiawei Chen, Liping Tang, Tao Zhang, Convergence of a new nonmonotone memory gradient method for unconstrained multiobjective optimization via robust approach
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DOI: 10.23952/jnva.8.2024.4.09
Volume 8, Issue 4, 1 August 2024, Pages 625-639
Abstract. Robust approach is a special scalarization method to deal with multiobjective optimization problems in the worst-case. In this paper, we propose a new non-monotone gradient type algorithm for solving unconstrained multiobjective optimization problems by the conjugate technique and the robust approach. The proposed method has a memory gradient property since the search direction is constructed by using the current descent direction and the past multi-step iterative descent directions. For this, the search direction is called a memory gradient search direction. The step-size is computed by the non-monotone linear search. A lower bound of the stepsize is presented under some mild conditions. Then the iterative sequence generated by the proposed method is proved to be convergent to a Pareto critical point of the multiobjective optimization problem under some mild conditions. Numerical experiments are reported to show the effectiveness of the proposed method.
How to Cite this Article:
Y. Bai, J. Chen, L. Tang, T. Zhang, Convergence of a new nonmonotone memory gradient method for unconstrained multiobjective optimization via robust approach, J. Nonlinear Var. Anal. 8 (2024), 625-639.