Distance Functions in Some Class of Infinite Dimensional Vector Spaces

This paper considers the problem of measuring technical efficiency in some class of normed vector spaces. Specifically, the paper focuses on preordered and partially ordered vector spaces by proposing a suitable encompassing netput formulation of the production possibility set. Duality theorems exte...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 201; no. 2; pp. 899 - 931
Main Authors: Anne, Bator, Briec, Walter
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2024
Springer Nature B.V
Springer Verlag
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Duality theorem
Efficiency
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Vector spaces
Vector-distance functions
90C46
Efficiency
Netput production vectors
Directional distance functions
Normed distance functions
49N15
Preordered normed vector spaces
Riesz vector spaces
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This paper considers the problem of measuring technical efficiency in some class of normed vector spaces. Specifically, the paper focuses on preordered and partially ordered vector spaces by proposing a suitable encompassing netput formulation of the production possibility set. Duality theorems extending some earlier results are established in the context of infinite dimensional spaces. The paper considers directional and normed distance functions and analyzes their relationships. Among other things, overall efficiency can be derived from technical efficiency under a suitable preordered vector space structure. More importantly, it is shown that the existence of core points in partially ordered vector spaces guarantees the comparison of production vectors using the directional distance function. Although the interior of the positive cone may be empty in infinite dimensional vector spaces, it is shown that normed distance functions can also be used to measure efficiency in such spaces by providing them with a suitable preorder structure.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02425-2