Geometrical and Topological Properties of a Parameterized Binary Relation in Vector Optimization

Christian Sommer ()
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Christian Sommer: Angewandte Mathematik 2, Universität Erlangen-Nürnberg

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 8, 815-840

Abstract: Abstract In real linear spaces, partial orderings are usually generated by ordering cones. In many situations, however, such an ordering cone is too small with respect to the whole space. Therefore, in this paper, we extend the concept of ordering cones to a more general concept. For this purpose, we define a parameterized binary relation, based on a convex cone and a binary function. We investigate some geometrical and topological properties of this relation in detail.

Keywords: Parameterized binary relation; Positive and negative semidefinite operators; Partial ordering; 41A50; 41A10; 41A15 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-014-0529-3

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