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Journal of Global Optimization

, Volume 52, Issue 1, pp 79–94 | Cite as

Characterizations for solidness of dual cones with applications

  • Y. Chiang
Article

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.

Keywords

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

Mathematics Subject Classification (2000)

52A07 90C33 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Sun Yat-sen UniversityKaohsiungTaiwan, R.O.C.

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