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Robust solutions to uncertain linear complementarity problems

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Abstract

In this paper, we adopt the robust optimization method to consider linear complementarity problems in which the data is not specified exactly or is uncertain, and it is only known to belong to a prescribed uncertainty set. We propose the notion of the ρ-robust counterpart and the ρ-robust solution of uncertain linear complementarity problems. We discuss uncertain linear complementarity problems with three different uncertainty sets, respectively, including an unknown-but-bounded uncertainty set, an ellipsoidal uncertainty set and an intersection-of-ellipsoids uncertainty set, and present some sufficient and necessary (or sufficient) conditions which ρ-robust solutions satisfy. Some special cases are investigated in this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Tongji University, Shanghai, 200092, China

    Dan Wu

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ji-ye Han

  3. Department of Mathematics, Tongji University, Shanghai, 200092, China

    Jing-hao Zhu

Authors
  1. Dan Wu
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  2. Ji-ye Han
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  3. Jing-hao Zhu
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Corresponding author

Correspondence to Dan Wu.

Additional information

Supported by the National Natural Science Foundation of China (No.10671010, 10871144 and 10671145).

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Wu, D., Han, Jy. & Zhu, Jh. Robust solutions to uncertain linear complementarity problems. Acta Math. Appl. Sin. Engl. Ser. 27, 339–352 (2011). https://doi.org/10.1007/s10255-010-0033-y

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  • DOI: https://doi.org/10.1007/s10255-010-0033-y

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