Adaptive Generalized Conditional Gradient Method for Multiobjective Optimization

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 op...

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Vydáno v:Journal of optimization theory and applications Ročník 206; číslo 1; s. 13
Hlavní autoři: Gebrie, Anteneh Getachew, Fukuda, Ellen Hidemi
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.07.2025
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Critical point
Engineering
Mathematics
Mathematics and Statistics
Methods
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Pareto optimization
Pareto optimum
Simplex method
Theory of Computation
Line search technique
Conditional gradient method
Multiobjective optimization
Frank-Wolfe
Descent direction
ISSN:0022-3239, 1573-2878
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02691-8