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Characterizations for solidness of dual cones with applications

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Abstract

In this paper, some characterizations for the solidness of dual cones are established. As applications, we prove that a Banach space is reflexive if it contains a solid pointed closed convex cone having a weakly compact base, and prove an analogue of a Karamardian’s result for the linear complementarity problem in reflexive Banach spaces. The uniqueness of the solution of the linear complementarity problem is also discussed.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan, R.O.C.

    Y. Chiang

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  1. Y. Chiang
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Correspondence to Y. Chiang.

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This work was partially supported by grants from the National Science Council of the Republic of China.

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Chiang, Y. Characterizations for solidness of dual cones with applications. J Glob Optim 52, 79–94 (2012). https://doi.org/10.1007/s10898-011-9684-3

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  • DOI: https://doi.org/10.1007/s10898-011-9684-3

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