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Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs

Author

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  • Duong Thi Viet An

    (Thai Nguyen University of Sciences
    Vietnam Academy of Science and Technology)

Abstract

Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming problems in Banach spaces are established in this paper. Since the decomposition procedures using orthogonality relations in Euclidean spaces and the compactness of finite-dimensional unit spheres, which worked well for finite-dimensional quadratic programs, cannot be applied to the Banach space setting, a series of new constructions and arguments are proposed. These results give a comprehensive extension of the corresponding theorems on finite-dimensional quadratic programs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:2:d:10.1007_s10957-021-01967-z
    DOI: 10.1007/s10957-021-01967-z
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    References listed on IDEAS

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    1. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2011. "Properties of two DC algorithms in quadratic programming," Journal of Global Optimization, Springer, vol. 49(3), pages 481-495, March.
    2. 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.
    3. 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.
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