Convex Cones

  • George Isac
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 41)


In the study of complementarity problems, an important mathematical tool is the concept of convex cone. In this book, the convex cones will be considered in a real vector space endowed with a locally convex topology. Such spaces will be the Euclidean space (R , <·,·>) a Hilbert space (E, <·,·>), a Banach space \( \left( {E\left\| \cdot \right\|} \right) \), or a locally convex space \( \left( {E\left( \tau \right),{\kern 1pt} {{\left\{ {{p_\alpha }} \right\}}_{\alpha \in A}}} \right) \) endowed with a topology τ defined by a sufficient family of seminorms \( {\left\{ {{p_\alpha }} \right\}_{\alpha \in A}} \). In this chapter, after some preliminaries, the basic notions on cones and the most important kinds of convex cones, necessary in the study of complementarity problems, will be introduced and studied.


Banach Space Complementarity Problem Convex Cone Arbitrary Element Topological Vector Space 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • George Isac
    • 1
  1. 1.Department of Mathematics and Computer ScienceRoyal Military College of CanadaKingstonCanada

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