Robust solutions to uncertain linear complementarity problems |
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Authors: | Dan Wu Ji-ye Han Jing-hao Zhu |
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Institution: | Dan Wu~1,Ji-ye Han~2,Jing-hao Zhu~3 1 Department of Applied Mathematics,Tongji University,Shanghai 200092,China 2 Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China 3 Department of Mathematics,China |
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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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Keywords: | uncertain linear complementarity problems robust optimization technology uncertainty set p- robust solution |
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