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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Puente, R., Vera de Serio, V.N. Locally Farkas-Minkowski linear inequality systems. Top 7, 103–121 (1999). https://doi.org/10.1007/BF02564714
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DOI: https://doi.org/10.1007/BF02564714
Key Words
- semi-infinite linear inequality systems
- Farkas-Minkowski systems
- locally polyhedral systems
- semi-infinite linear programming