Primal-dual stability in continuous linear optimization

• 成果类型: Article; Proceedings Paper
• 署名作者: Goberna, Miguel A.; Todorov, Maxim I.
• 署名单位: Universitat d'Alacant; Universidad Americas Puebla (UDLAP)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0128-2
• 发表日期: 2009
• 页码: 129-146
• 关键词: inequality systems; model-reduction; semiinfinite; CONVERGENCE; uniqueness; distance; set

摘要

Any linear (ordinary or semi-infinite) optimization problem, and also its dual problem, can be classified as either inconsistent or bounded or unbounded, giving rise to nine duality states, three of them being precluded by the weak duality theorem. The remaining six duality states are possible in linear semi-infinite programming whereas two of them are precluded in linear programming as a consequence of the existence theorem and the non-homogeneous Farkas Lemma. This paper characterizes the linear programs and the continuous linear semi-infinite programs whose duality state is preserved by sufficiently small perturbations of all the data. Moreover, it shows that almost all linear programs satisfy this stability property.