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Affine Variational Inequalities on Normed Spaces

Author

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  • Nguyen Dong Yen

    (Vietnam Academy of Science and Technology)

  • Xiaoqi Yang

    (Department of Applied Mathematics, The Hong Kong Polytechnic University)

Abstract

This paper studies infinite-dimensional affine variational inequalities on normed spaces. It is shown that infinite-dimensional quadratic programming problems and infinite-dimensional linear fractional vector optimization problems can be studied by using affine variational inequalities. We present two basic facts about infinite-dimensional affine variational inequalities: the Lagrange multiplier rule and the solution set decomposition.

Suggested Citation

  • Nguyen Dong Yen & Xiaoqi Yang, 2018. "Affine Variational Inequalities on Normed Spaces," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 36-55, July.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:1:d:10.1007_s10957-018-1296-3
    DOI: 10.1007/s10957-018-1296-3
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    References listed on IDEAS

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    1. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    2. Nguyen Thanh Qui, 2012. "Nonlinear Perturbations of Polyhedral Normal Cone Mappings and Affine Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 98-122, April.
    3. Shu Lu & Stephen M. Robinson, 2008. "Variational Inequalities over Perturbed Polyhedral Convex Sets," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 689-711, August.
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    Cited by:

    1. N. T. T. Huong & J.-C. Yao & N. D. Yen, 2020. "Geoffrion’s proper efficiency in linear fractional vector optimization with unbounded constraint sets," Journal of Global Optimization, Springer, vol. 78(3), pages 545-562, November.
    2. Duong Thi Viet An, 2022. "Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 426-442, February.
    3. D. T. V. An & N. D. Yen, 2021. "Optimality conditions based on the Fréchet second-order subdifferential," Journal of Global Optimization, Springer, vol. 81(2), pages 351-365, October.

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