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Hadamard Directional Differentiability of the Optimal Value Function of a Quadratic Programming Problem

Author

Listed:
  • Sainan Zhang

    (Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Liwei Zhang

    (Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Hongwei Zhang

    (Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Qingsong Duan

    (Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

Abstract

In this paper, we consider the stability analysis of a convex quadratic programming (QP) problem and its restricted Wolfe dual when all parameters in the problem are perturbed. Based on the continuity of the feasible set mapping, we establish the upper semi-continuity of the optimal solution mappings of the convex QP problem and the restricted Wolfe dual problem. Furthermore, by characterizing the optimal value function as a min–max optimization problem over two compact convex sets, we demonstrate the Lipschitz continuity and the Hadamard directional differentiability of the optimal value function.

Suggested Citation

  • Sainan Zhang & Liwei Zhang & Hongwei Zhang & Qingsong Duan, 2018. "Hadamard Directional Differentiability of the Optimal Value Function of a Quadratic Programming Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(03), pages 1-22, June.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:03:n:s0217595918500124
    DOI: 10.1142/S0217595918500124
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    Cited by:

    1. Qingsong Duan & Mengwei Xu & Shaoyan Guo & Liwei Zhang, 2018. "Quantitative Stability of Two-Stage Linear Second-Order Conic Stochastic Programs with Full Random Recourse," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-24, October.

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