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<p>In this paper, we propose a nonmonotone line search algorithm for constrained multi-objective optimization problems and analyze its global convergence. This method is a generalization of the nonmonotone method proposed by Zhou (Appl Numer Math 91:75–88, 2015) in the scalar case to the constrained multi-objective optimization problem. In the construction of the subproblem for computing the search direction, we use a diagonal matrix approximation instead of the Hessian and use the convex combination of the function values instead of the maximum function or the average of the successive previous function values as the nonmonotone term in the nonmonotone line search similarly to the algorithm of Zhou (2015). Under suitable assumptions, it is proved that the proposed algorithm has global convergence. Finally, some numerical experiment results are given to demonstrate the efficiency of our algorithm compared with some existing algorithms.</p>

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A nonmonotone line search method for constrained multiobjective optimization problems

  • 期刊论文

  • 发表日期：

    2025年8月2日

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  • Wonchol Hwang,
  • Yunchol Jong,
  • Chungil Kim

摘要

In this paper, we propose a nonmonotone line search algorithm for constrained multi-objective optimization problems and analyze its global convergence. This method is a generalization of the nonmonotone method proposed by Zhou (Appl Numer Math 91:75–88, 2015) in the scalar case to the constrained multi-objective optimization problem. In the construction of the subproblem for computing the search direction, we use a diagonal matrix approximation instead of the Hessian and use the convex combination of the function values instead of the maximum function or the average of the successive previous function values as the nonmonotone term in the nonmonotone line search similarly to the algorithm of Zhou (2015). Under suitable assumptions, it is proved that the proposed algorithm has global convergence. Finally, some numerical experiment results are given to demonstrate the efficiency of our algorithm compared with some existing algorithms.