Adaptive Generalized Conditional Gradient Method for Multiobjective Optimization

Anteneh Getachew Gebrie () and Ellen Hidemi Fukuda ()
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Anteneh Getachew Gebrie: Perimeter Institute for Theoretical Physics
Ellen Hidemi Fukuda: Kyoto University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 12, 27 pages

Abstract: Abstract In this paper, we propose a generalized conditional gradient method for multiobjective optimization, where the objective function is the sum of a smooth function and a possibly nonsmooth function. The proposed method is an improved extension of the classical Frank-Wolfe method of single-objective optimization to the multiobjective optimization problem. The method combines the so-called normalized descent direction as an adaptive procedure and the line search technique. We prove the convergence of the algorithm with respect to Pareto optimality under mild assumptions. The iteration complexity for obtaining an approximate Pareto critical point and the convergence rate in terms of a merit function is also analyzed. Finally, we report some numerical results, which demonstrate the feasibility and competitiveness of the proposed method.

Keywords: Multiobjective optimization; Conditional gradient method; Frank-Wolfe; Descent direction; Line search technique (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02691-8

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