Paper Info
Title
Stability and Well-Posedness in Linear Semi-Infinite Programming
Abstract
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.
Year
DOI
Venue
1999
10.1137/S1052623497319869
SIAM Journal on Optimization
Keywords
Field
DocType
linear semi-infinite programming,optimal value function,set indexing,stability property,optimal set,index set,lower semicontinuity,optimal set mapping,hadamard well-posedness,high stability,feasible set mapping,stability
Set function,Discrete mathematics,Mathematical optimization,Active set method,Semi-infinite programming,Index set,Bellman equation,Feasible region,Parameter space,Hadamard transform,Mathematics
Journal
Volume
Issue
ISSN
10
1
1052-6234
Citations 
PageRank 
References 
16
1.68
3
Authors
4
Name
Order
Citations
PageRank
M. J. Cánovas110912.48
M. A. López2374.48
J. Parra3374.48
M. I. Todorov4465.67