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Newton-like methods for efficient solutions in vector optimization

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  • Thai Chuong

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. Copyright Springer Science+Business Media, LLC 2013

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  • Thai Chuong, 2013. "Newton-like methods for efficient solutions in vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 495-516, April.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:3:p:495-516
    DOI: 10.1007/s10589-012-9495-6
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    4. L. C. Ceng & B. S. Mordukhovich & J. C. Yao, 2010. "Hybrid Approximate Proximal Method with Auxiliary Variational Inequality for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 267-303, August.
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    1. Gonçalves, M.L.N. & Lima, F.S. & Prudente, L.F., 2022. "A study of Liu-Storey conjugate gradient methods for vector optimization," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    2. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram, 2020. "On q -Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    3. M. L. N. Gonçalves & L. F. Prudente, 2020. "On the extension of the Hager–Zhang conjugate gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 889-916, July.
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    6. Qing-Rui He & Chun-Rong Chen & Sheng-Jie Li, 2023. "Spectral conjugate gradient methods for vector optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 457-489, November.

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