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Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

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Abstract

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.

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Authors and Affiliations

  1. Department of Scientific Computing and Applied Software, Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, China

    Zhi-ping Chen & You-pan Han

Authors
  1. Zhi-ping Chen
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  2. You-pan Han
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Correspondence to Zhi-ping Chen.

Additional information

Supported by the National Natural Science Foundation of China (10571141,70971109) and the Key Project of the National Natural Science Foundation of China (70531030).

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Chen, Zp., Han, Yp. Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs. Appl. Math. J. Chin. Univ. 25, 391–399 (2010). https://doi.org/10.1007/s11766-010-2202-4

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  • DOI: https://doi.org/10.1007/s11766-010-2202-4

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