A generalized conditional gradient method for multiobjective composite optimization problems

This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these problems, we propose a generalized version of the conditional g...

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Published in:Optimization Vol. 74; no. 2; pp. 473 - 503
Main Authors: Assunção, P. B., Ferreira, O. P., Prudente, L. F.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 25.01.2025
Taylor & Francis LLC
Subjects:
Asymptotic methods
Conditional gradient method
constrained optimization problem
Convexity
Frank-Wolfe method
multiobjective optimization
Multiple objective analysis
Optimization
Pareto optimality
ISSN:0233-1934, 1029-4945
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Abstract This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these problems, we propose a generalized version of the conditional gradient method, also known as Frank-Wolfe method. The method is analysed with three step size strategies, including Armijo-type, adaptive, and diminishing step sizes. We establish asymptotic convergence properties and iteration-complexity bounds, with and without convexity assumptions on the objective functions. Numerical experiments illustrating the practical behaviour of the methods are presented.
AbstractList This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these problems, we propose a generalized version of the conditional gradient method, also known as Frank-Wolfe method. The method is analysed with three step size strategies, including Armijo-type, adaptive, and diminishing step sizes. We establish asymptotic convergence properties and iteration-complexity bounds, with and without convexity assumptions on the objective functions. Numerical experiments illustrating the practical behaviour of the methods are presented.
Author Prudente, L. F.
Ferreira, O. P.
Assunção, P. B.
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  surname: Prudente
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  organization: Universidade Federal de Goiás
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SubjectTerms Asymptotic methods
Conditional gradient method
constrained optimization problem
Convexity
Frank-Wolfe method
multiobjective optimization
Multiple objective analysis
Optimization
Pareto optimality
Title A generalized conditional gradient method for multiobjective composite optimization problems
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