Paper Info
Title
Distance to Solvability/Unsolvability in Linear Optimization
Abstract
In this paper we measure how much a linear optimization problem, in $\mathbb{R}^n$, has to be perturbed in order to lose either its solvability (i.e., the existence of optimal solutions) or its unsolvability property. In other words, if we consider as ill-posed those problems in the boundary of the set of solvable ones, then we can say that this paper deals with the associated distance to ill-posedness. Our parameter space is the set of all the linear semi-infinite programming problems with a fixed, but arbitrary, index set. In this framework, which includes as a particular case the ordinary linear programming, we obtain a formula for the distance from a solvable problem to unsolvability in terms of the nominal problem's coefficients. Moreover, this formula also provides the exact expression, or a lower bound, of the distance from an unsolvable problem to solvability. The relationship between the solvability and the primal-dual consistency is analyzed in the semi-infinite context, underlining the differences with the finite case.
Year
DOI
Venue
2006
10.1137/040612981
SIAM Journal on Optimization
Keywords
Field
DocType
ordinary linear programming,paper deal,solvable problem,solv- ability,finite case,distance to ill-posedness,stability,ill-posedness,linear semi-infinite programming.,linear semi-infinite programming problem,linear optimization,index set,unsolvable problem,linear optimization problem,nominal problem,associated distance,lower bound,indexation,linear program,parameter space,duality
Linear optimization problem,Discrete mathematics,Mathematical optimization,Upper and lower bounds,Index set,Duality (optimization),Linear programming,Parameter space,Mathematics
Journal
Volume
Issue
ISSN
16
3
1052-6234
Citations 
PageRank 
References 
6
0.61
13
Authors
4
Name
Order
Citations
PageRank
M. J. Cánovas110912.48
M. A. López2374.48
J. Parra3374.48
F. J. Toledo460.61