An away-step Frank–Wolfe algorithm for constrained multiobjective optimization

Douglas S. Gonçalves (), Max L. N. Gonçalves () and Jefferson G. Melo ()
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Douglas S. Gonçalves: Universidade Federal de Santa Catarina
Max L. N. Gonçalves: IME, Universidade Federal de Goiás
Jefferson G. Melo: IME, Universidade Federal de Goiás

Computational Optimization and Applications, 2024, vol. 88, issue 3, No 2, 759-781

Abstract: Abstract In this paper, we propose and analyze an away-step Frank–Wolfe algorithm designed for solving multiobjective optimization problems over polytopes. We prove that each limit point of the sequence generated by the algorithm is a weak Pareto optimal solution. Furthermore, under additional conditions, we show linear convergence of the whole sequence to a Pareto optimal solution. Numerical examples illustrate a promising performance of the proposed algorithm in problems where the multiobjective Frank–Wolfe convergence rate is only sublinear.

Keywords: Frank–Wolfe algorithm; Conditional gradient method; Away-step; Linear convergence rate; Pareto optimality; Constrained multiobjective problem; 49M05; 58E17; 65K05; 90C29 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00577-5

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