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

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  • Christian Sommer

    (Angewandte Mathematik 2, Universität Erlangen-Nürnberg)

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.

Suggested Citation

  • Christian Sommer, 2014. "Geometrical and Topological Properties of a Parameterized Binary Relation in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 815-840, December.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:3:d:10.1007_s10957-014-0529-3
    DOI: 10.1007/s10957-014-0529-3
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    References listed on IDEAS

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    1. Gabriele Eichfelder, 2011. "Optimal Elements in Vector Optimization with a Variable Ordering Structure," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 217-240, November.
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    Cited by:

    1. C. Zălinescu, 2016. "On Second-Order Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 802-829, March.

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