Technical efficiency and distance to a reverse convex set |
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| Institution: | 1. Université de Rennes, Rennes, France;2. Université de Montpellier, Sciences et Techniques du Languedoc, Institut de Mathematiques, Place Eugene Bataillon, 34060 Montpellier Cedex, France;1. School of Informatics, Xiamen University, China;2. School of Computer Engineering, Jimei University, China;3. Department of Computer Science, University of Sheffield, UK |
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| Abstract: | The problem of finding the distance to a reverse (or complement of a) convex subset in a normed vector space is considered. This nonconvex and, in general, nonsmooth optimization problem arises in quantitative economics in the theory of measuring the technical efficiency of production units. In this context, applying a suitable duality theorem similar to the Nirenberg's one known for the distance to a convex subset, the problem reduces to a finite number of independent linear programming problems. |
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