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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Vydáno v:	Optimization Ročník 74; číslo 2; s. 473 - 503
Hlavní autoři:	Assunção, P. B., Ferreira, O. P., Prudente, L. F.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Philadelphia Taylor & Francis 25.01.2025 Taylor & Francis LLC
Témata:	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
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0233-1934 1029-4945
DOI:	10.1080/02331934.2023.2257709