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Existence of Solutions for Vector Optimization on Hadamard Manifolds

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  • Li-Wen Zhou

    (Sichuan University)

  • Nan-Jing Huang

    (Sichuan University)

Abstract

In this paper, a relationship between a vector variational inequality and a vector optimization problem is given on a Hadamard manifold. An existence of a weak minimum for a constrained vector optimization problem is established by an analogous to KKM lemma on a Hadamard manifold.

Suggested Citation

  • Li-Wen Zhou & Nan-Jing Huang, 2013. "Existence of Solutions for Vector Optimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 44-53, April.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:1:d:10.1007_s10957-012-0186-3
    DOI: 10.1007/s10957-012-0186-3
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    References listed on IDEAS

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    1. Jonathan M. Borwein, 1983. "On the Existence of Pareto Efficient Points," Mathematics of Operations Research, INFORMS, vol. 8(1), pages 64-73, February.
    2. Ruiz-Garzon, G. & Osuna-Gomez, R. & Rufian-Lizana, A., 2004. "Relationships between vector variational-like inequality and optimization problems," European Journal of Operational Research, Elsevier, vol. 157(1), pages 113-119, August.
    3. M. Oveisiha & J. Zafarani, 2012. "Vector optimization problem and generalized convexity," Journal of Global Optimization, Springer, vol. 52(1), pages 29-43, January.
    4. S. Deng, 1998. "Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 123-131, January.
    5. O. Ferreira & L. Pérez & S. Németh, 2005. "Singularities of Monotone Vector Fields and an Extragradient-type Algorithm," Journal of Global Optimization, Springer, vol. 31(1), pages 133-151, January.
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    Citations

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    Cited by:

    1. Xiangmei Wang & Chong Li & Jen-Chih Yao, 2016. "On Some Basic Results Related to Affine Functions on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 783-803, September.
    2. Dumitru Motreanu & Van Thien Nguyen & Shengda Zeng, 2020. "Existence of Solutions for Implicit Obstacle Problems of Fractional Laplacian Type Involving Set-Valued Operators," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 391-407, November.
    3. Alexandru Kristály & Chong Li & Genaro López-Acedo & Adriana Nicolae, 2016. "What Do ‘Convexities’ Imply on Hadamard Manifolds?," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1068-1074, September.
    4. Xiao-bo Li & Li-wen Zhou & Nan-jing Huang, 2016. "Gap Functions and Global Error Bounds for Generalized Mixed Variational Inequalities on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 830-849, March.
    5. E. E. A. Batista & G. C. Bento & O. P. Ferreira, 2015. "An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 550-557, November.

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