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Conditional gradient method for multiobjective optimization

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Abstract

We analyze the conditional gradient method, also known as Frank–Wolfe method, for constrained multiobjective optimization. The constraint set is assumed to be convex and compact, and the objectives functions are assumed to be continuously differentiable. The method is considered with different strategies for obtaining the step sizes. Asymptotic convergence properties and iteration-complexity bounds with and without convexity assumptions on the objective functions are stablished. Numerical experiments are provided to illustrate the effectiveness of the method and certify the obtained theoretical results.

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Acknowledgements

This work was funded by FAPEG (Grants PRONEM-201710267000532, PPP03/15-201810267001725), CNPq (Grants 305158/2014-7, 08151/2016-1, 302473/2017-3, 424860/2018-0), and CAPES.

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  1. Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, GO, CEP 74001-970, Brazil

    P. B. Assunção, O. P. Ferreira & L. F. Prudente

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  1. P. B. Assunção
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Assunção, P.B., Ferreira, O.P. & Prudente, L.F. Conditional gradient method for multiobjective optimization. Comput Optim Appl 78, 741–768 (2021). https://doi.org/10.1007/s10589-020-00260-5

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