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Newton-like methods for efficient solutions in vector optimization

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Abstract

In this work we study the Newton-like methods for finding efficient solutions of the vector optimization problem for a map from a finite dimensional Hilbert space X to a Banach space Y, with respect to the partial order induced by a closed, convex and pointed cone C with a nonempty interior. We present both exact and inexact versions, in which the subproblems are solved approximately, within a tolerance. Furthermore, we prove that under reasonable hypotheses, the sequence generated by our method converges to an efficient solution of this problem.

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Acknowledgements

The author would like to thank the referees for valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics & Applications, Saigon University, 273 An Duong Vuong Street, Ward 3, District 5, Hochiminh City, Vietnam

    Thai Doan Chuong

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  1. Thai Doan Chuong
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Correspondence to Thai Doan Chuong.

Additional information

This work was supported by a research grant from the National Foundation for Science and Technology Development of Vietnam (NAFOSTED).

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Chuong, T.D. Newton-like methods for efficient solutions in vector optimization. Comput Optim Appl 54, 495–516 (2013). https://doi.org/10.1007/s10589-012-9495-6

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  • DOI: https://doi.org/10.1007/s10589-012-9495-6

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