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Convex Cones, Minimality Notions, and Consequences

  • Conference paper
Recent Advances and Historical Development of Vector Optimization

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 294))

Abstract

Most problems to which functional analysis applies can be modelled by

$$h(b)={{\min }_{s}}\{f(x):g(x){{s}_{p}}b\}$$
(VP)

where X. Y. Z are vector spaces. S and P are appropriate closed convex cones. and f:X→Y,S and g:X→Z,P are convex, Lipschitz, differentiable or otherwise. [y ≤p b means b − y ∈ P]

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Author information

Authors and Affiliations

  1. Dalhousie University, Halifax, Nova Scotia, Canada

    J. M. Borwein

Authors
  1. J. M. Borwein
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Editor information

Editors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, D-8520, Erlangen, Germany

    Johannes Jahn

  2. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstr. 7, D-6100, Darmstadt, Germany

    Werner Krabs

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© 1987 Springer-Verlag Berlin Heidelberg

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Borwein, J.M. (1987). Convex Cones, Minimality Notions, and Consequences. In: Jahn, J., Krabs, W. (eds) Recent Advances and Historical Development of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46618-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-46618-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18215-3

  • Online ISBN: 978-3-642-46618-2

  • eBook Packages: Springer Book Archive

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