On Solidness of Polar Cones

J. H. Qu

Journal of Optimization Theory and Applications, 2001, vol. 109, issue 1, No 11, 199-214

Abstract: Abstract We investigate the properties of cones whose polars are solid in different polar topologies. By a standard duality argument, we obtain a number of necessary and sufficient conditions for closed convex cones to be solid in various locally convex spaces. From this, we can deduce easily the extensions of previous related results. Furthermore, we construct a class of closed convex cones in some Banach spaces, which are not solid but whose polars satisfy the angle property. This solves the Han conjecture in the negative.

Keywords: convex cones; polars of cones; bases of cones; solid cones; angle property (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017574123926

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