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Complexity bound of trust-region methods for convex smooth unconstrained multiobjective optimization

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Abstract

In this paper, we analyze the worst-case complexity of trust-region methods for solving unconstrained smooth multiobjective optimization problems. We particularly focus on the method proposed by Villacorta et al. [J Optim Theory Appl 160:865–889, 2014]. When the component functions are convex (respectively strongly convex), we will derive a complexity bound of \({\mathcal {O}}(\epsilon ^{-1})\) (respectively \({\mathcal {O}}(\log \epsilon ^{-1})\)) for driving some criticality measure below some given positive \(\epsilon\). The derived complexity bounds recover those of classical trust-region methods for solving (strongly) convex smooth unconstrained single-objective problems.

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Acknowledgements

The author is very grateful to two anonymous referees for very helpful and constructive comments, which significantly improved the contributions and presentation of the paper.

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  1. Center for Mathematics and Applications (NovaMath), FCT NOVA, 2829-516, Caparica, Portugal

    R. Garmanjani

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  1. R. Garmanjani
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Support for the author was provided by Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) under the projects PTDC/MAT-APL/28400/2017, UIDP/MAT/00297/2020, and UIDB/MAT/00297/2020.

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Garmanjani, R. Complexity bound of trust-region methods for convex smooth unconstrained multiobjective optimization. Optim Lett 17, 1161–1179 (2023). https://doi.org/10.1007/s11590-022-01932-3

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