Characterizing Efficiency on Infinite-dimensional Commodity Spaces with Ordering Cones Having Possibly Empty Interior

Some production models in finance require infinite-dimensional commodity spaces, where efficiency is defined in terms of an ordering cone having possibly empty interior. Since weak efficiency is more tractable than efficiency from a mathematical point of view, this paper characterizes the equality b...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2015-02, Vol.164 (2), p.455-478
Main Authors: Flores-Bazán, Fabián, Flores-Bazán, Fernando, Laengle, Sigifredo
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Commodities
Computational efficiency
Computing time
Cones
Efficiency
Engineering
Lagrange multiplier
Mathematical analysis
Mathematical functions
Mathematical models
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Order disorder
Preferences
Studies
Theory of Computation
Vector space
Vectors (mathematics)
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Summary:Some production models in finance require infinite-dimensional commodity spaces, where efficiency is defined in terms of an ordering cone having possibly empty interior. Since weak efficiency is more tractable than efficiency from a mathematical point of view, this paper characterizes the equality between efficiency and weak efficiency in infinite-dimensional spaces without further assumptions, like closedness or free disposability. This is obtained as an application of our main result that characterizes the solutions to a unified vector optimization problem in terms of its scalarization. Standard models as efficiency, weak efficiency (defined in terms of quasi-relative interior), weak strict efficiency, strict efficiency, or strong solutions are carefully described. In addition, we exhibit two particular instances and compute the efficient and weak efficient solution set in Lebesgue spaces.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-014-0558-y