Comments on: Stability in linear optimization and related topics. A personal tour 7
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Virginia N. Vera de Serio [1]
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[1] Universidad Nacional de Cuyo
Universidad Nacional de Cuyo
Argentina
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- Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 20, Nº. 2, 2012, págs. 267-269
- Idioma: inglés
- Enlaces
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Resumen
This is an excellent survey of several topics in stability in linear programming. Here stability refers to some properties, conveniently stated, that are maintained under small perturbations of the data of the nominal optimization problem. It is important to realize that the stability properties analyzed are related to the representation of the linear optimization problem through some constraint system and some objective function, where the special characteristics of its feasible set play no role. This is in this way because any closed convex set can be expressed as the feasible set of some linear constraint system. Moreover, for any closed convex set there is always a very stable representation through a convenient linear constraint system, and it is also possible to exhibit a very unstable representation (see Goberna et al. (2003) for a discussion and examples).
