Stability and well-posedness in linear semi-infinite programming

作     者：Cánovas, MJ López, MA Parra, J Todorov, MI 

作者机构：Miguel Hernandez Univ Dept Appl Math & Stat Alicante 03202 Spain Univ Alicante Dept Stat & Operat Res Alicante 03071 Spain Bulgarian Acad Sci Inst Math Plovdiv 4002 Bulgaria 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 (工业与应用数学会最优化杂志)

年 卷 期：1999年第10卷第1期

页      面：82-98页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：stability Hadamard well-posedness semi-infinite programming feasible set mapping optimal set mapping optimal value function 

摘      要：This paper presents an approach to the stability and the Hadamard well-posedness of the linear semi-infinite programming problem (LSIP). No standard hypothesis is required in relation to the set indexing of the constraints and, consequently, the functional dependence between the linear constraints and their associated indices has no special property. We consider, as parameter space, the set of all LSIP problems whose constraint systems have the same index set, and we define in it an extended metric to measure the size of the perturbations. Throughout the paper the behavior of the optimal value function and of the optimal set mapping are analyzed. Moreover, a certain type of Hadamard well-posedness, which does not require the boundedness of the optimal set, is characterized. The main results provided in the paper allow us to point out that the lower semicontinuity of the feasible set mapping entails high stability of the whole problem, mainly when this property occurs simultaneously with the boundedness of the optimal set. In this case all the stability properties hold, with the only exception being the lower semicontinuity of the optimal set mapping.