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Existence Results for Minimal Points

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Set-valued Optimization

Part of the book series: Vector Optimization ((VECTOROPT))

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Abstract

In this chapter we establish several existence results for minimal points with respect to transitive relations; then we apply them in topological vector spaces for quasiorders generated by convex cones. We continue with the presentation of several types of convex cones and compactness notions with respect to cones. We end the chapter with existence results for vector and set optimization problems.

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Authors and Affiliations

  1. Rochester Institute of Technology School of Mathematical Sciences, Rochester, New York, USA

    Akhtar A. Khan

  2. Halle, Germany

    Christiane Tammer

  3. Faculty of Mathematics, University “Al. I. Cuza” Iasi, Iasi, Romania

    Constantin Zălinescu

Authors
  1. Akhtar A. Khan
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  2. Christiane Tammer
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  3. Constantin Zălinescu
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Khan, A.A., Tammer, C., Zălinescu, C. (2015). Existence Results for Minimal Points. In: Set-valued Optimization. Vector Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54265-7_9

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