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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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
Keywords
- Base for convex cone
- Order-unit norm
- Minkowski functional
- Linear complementarity problem
- Globally solvable property