Locally Farkas-Minkowski linear inequality systems |
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Authors: | Rubén Puente Virginia N Vera de Serio |
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Institution: | (1) Departamento de Matemáticas Facultad de Ciencias Físico, Matemáticas y Naturales, Universidad Nacional de San Luis, Ejército de los Andes 950, 5700 San Luis, Argentina;(2) Facultad de Ciencias Económicas, Universidad Nacional de Cuyo Centro Universitario, 5500 Mendoza, Argentina |
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Abstract: | This paper introduces thelocally Farkas-Minkowski (LFM) linear inequality systems in a finite dimensional Euclidean space. These systems are those ones that satisfy that any consequence
of the system that is active at some solution point is also a consequence of some finite subsystem. This class includes the
Farkas-Minkowski systems and verifies most of the properties that these systems possess. Moreover, it contains the locally
polyhedral systems, which are the natural external representation of quasi-polyhedral sets. TheLFM systems appear to be the natural external representation of closed convex sets. A characterization based on their properties
under the union of systems is provided. In linear semi-infinite programming, theLFM property is the more general constraint qualification such that the Karush-Kuhn-Tucker condition characterizes the optimal
points. Furthermore, the pair of Haar dual problems has no duality gap. |
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Keywords: | semi-infinite linear inequality systems Farkas-Minkowski systems locally polyhedral systems semi-infinite linear programming |
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