Some perturbation theory for linear programming
Mathematical Programming: Series A and B
Topological stability of linear semi-infinite inequality systems
Journal of Optimization Theory and Applications
Stability Theory for Linear Inequality Systems
SIAM Journal on Matrix Analysis and Applications
Stability Theory for Linear Inequality Systems II: Upper Semicontinuity of the Solution Set Mapping
SIAM Journal on Optimization
Stability and Well-Posedness in Linear Semi-Infinite Programming
SIAM Journal on Optimization
Distance to ill-posedness and the consistency value of linear semi-infinite inequality systems
Mathematical Programming: Series A and B
On the Stability of the Extreme Point Set in Linear Optimization
SIAM Journal on Optimization
Distance to Solvability/Unsolvability in Linear Optimization
SIAM Journal on Optimization
| Hi-index | 7.29 |
This paper deals with the stability of linear semi-infinite programming (LSIP, for short) problems. We characterize those LSIP problems from which we can obtain, under small perturbations in the data, different types of problems, namely, inconsistent, consistent unsolvable, and solvable problems. The problems of this class are highly unstable and, for this reason, we say that they are totally ill-posed. The characterization that we provide here is of geometrical nature, and it depends exclusively on the original data (i.e., on the coefficients of the nominal LSIP problem). Our results cover the case of linear programming problems, and they are mainly obtained via a new formula for the subdifferential mapping of the support function.