2024/11/14 by Maria Eduarda Pinheiro, Pinheiro, Maria Eduarda, Geovani Nunes Grapiglia +1 · 2 citations
Computer Science · #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Robotic Path Planning Algorithms
paper · pdf · doi:10.48550/arxiv.2411.09466
openalex publication_date 2024/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we propose a general nonmonotone line-search method for nonconvex multi\-objective optimization problems with convex constraints. At the kth iteration, the degree of nonmonotonicity is controlled by a vector νk with nonnegative components. Different choices for νk lead to different nonmonotone step-size rules. Assuming that the sequence \νk\k≥ 0 is summable, and that the ith objective function has Hölder continuous gradient with smoothness parameter θi ∈(0,1], we show that the proposed method takes no more than O(ε^-(1+\frac1θmin)) iterations to find a ε-approximate Pareto critical point for a problem with m objectives and θmin= mini=1,…, m \θi\. In particular, this complexity bound applies to the methods proposed by Drummond and Iusem (Comput. Optim. Appl. 28: 5--29, 2004), by Fazzio and Schuverdt (Optim. Lett. 13: 1365--1379, 2019), and by Mita, Fukuda and Yamashita (J. Glob. Optim. 75: 63--90, 2019). The generality of our approach also allows the development of new methods for multiobjective optimization. As an example, we propose a new nonmonotone step-size rule inspired by the Metropolis criterion. Preliminary numerical results illustrate the benefit of nonmonotone line searches and suggest that our new rule is particularly suitable for multiobjective problems in which at least one of the objectives has many non-global local minimizers.