Sufficient conditions for total ill-posedness in linear semi-infinite optimization

This paper deals with the so-called total ill-posedness of linear optimization problems with an arbitrary (possibly infinite) number of constraints. We say that the nominal problem is totally ill-posed if it exhibits the highest unstability in the sense that arbitrarily small perturbations of the pr...

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Bibliographic Details
Published in:	European journal of operational research Vol. 181; no. 3; pp. 1126 - 1136
Main Authors:	Cánovas, M.J., López, M.A., Parra, J., Toledo, F.J.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 16-09-2007 Elsevier Elsevier Sequoia S.A
Series:	European Journal of Operational Research
Subjects:	Finite element analysis Ill-posedness Linear programming Optimization Problem solving Semi-infinite programming Studies Semi-infinite programming Linear programming Ill-posedness
Online Access:	Get full text
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Summary:	This paper deals with the so-called total ill-posedness of linear optimization problems with an arbitrary (possibly infinite) number of constraints. We say that the nominal problem is totally ill-posed if it exhibits the highest unstability in the sense that arbitrarily small perturbations of the problem’s coefficients may provide both, consistent (with feasible solutions) and inconsistent problems, as well as bounded (with finite optimal value) and unbounded problems, and also solvable (with optimal solutions) and unsolvable problems. In this paper we provide sufficient conditions for the total ill-posedness property exclusively in terms of the coefficients of the nominal problem.
ISSN:	0377-2217 1872-6860
DOI:	10.1016/j.ejor.2005.04.055