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A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem

Author

Listed:
  • Jia Wu

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

  • Yi Zhang

    (Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai 200237, 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)

  • Yue Lu

    (School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, P. R. China)

Abstract

This paper is devoted to the study of solving method for a type of inverse linear semidefinite programming problem in which both the objective parameter and the right-hand side parameter of the linear semidefinite programs are required to adjust. Since such kind of inverse problem is equivalent to a mathematical program with semidefinite cone complementarity constraints which is a rather difficult problem, we reformulate it as a nonconvex semi-definte programming problem by introducing a nonsmooth partial penalty function to penalize the complementarity constraint. The penalized problem is actually a nonsmooth DC programming problem which can be solved by a sequential convex program approach. Convergence analysis of the penalty models and the sequential convex program approach are shown. Numerical results are reported to demonstrate the efficiency of our approach.

Suggested Citation

  • Jia Wu & Yi Zhang & Liwei Zhang & Yue Lu, 2016. "A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-26, August.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:04:n:s0217595916500251
    DOI: 10.1142/S0217595916500251
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    References listed on IDEAS

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    1. Ravindra K. Ahuja & James B. Orlin, 2001. "Inverse Optimization," Operations Research, INFORMS, vol. 49(5), pages 771-783, October.
    2. Jong-Shi Pang & Defeng Sun & Jie Sun, 2003. "Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 39-63, February.
    3. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, April.
    4. Jianzhong Zhang & Zhongfan Ma, 1999. "Solution Structure of Some Inverse Combinatorial Optimization Problems," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 127-139, July.
    5. Burkard, Rainer E. & Lin, Yixun & Zhang, Jianzhong, 2004. "Weight reduction problems with certain bottleneck objectives," European Journal of Operational Research, Elsevier, vol. 153(1), pages 191-199, February.
    6. L. Jeff Hong & Yi Yang & Liwei Zhang, 2011. "Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach," Operations Research, INFORMS, vol. 59(3), pages 617-630, June.
    7. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
    8. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
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