Lipschitz continuity of the optimal value via bounds on the optimal set in linear semi-infinite optimization

• 成果类型: Article
• 署名作者: Canovas, Maria J.; Lopez, Marco A.; Parra, Juan; Toledo, F. Javier
• 署名单位: Universidad Miguel Hernandez de Elche; Universitat d'Alacant
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1060.0198
• 发表日期: 2006
• 页码: 478-489
• 关键词: ill-posedness; distance; STABILITY

摘要

We consider the parametric space of all the linear semi-infinite programming problems with constraint systems having the same index set. Under a certain regularity condition, the so-called well-posedness with respect to the solvability, it is known from Canovas et a]. [2] that the optimal value function is Lipschitz continuous around the nominal problem pi. In this paper we obtain an explicit Lipschitz constant for such a function in a certain neighborhood of pi. We emphasize the fact that both the constant and the size of the neighborhood are exclusively expressed in terms of the nominal problem data, and that they involve the distances to primal and to dual inconsistency. Moreover, a uniform bound for the optimal set is provided. This bound constitutes a key ingredient to derive the Lipschitz constant for the optimal value function.