Sufficient conditions for total ill-posedness in linear semi-infinite optimization |
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Authors: | MJ Cánovas MA López J Parra FJ Toledo |
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Institution: | 1. Operations Research Center, Miguel Hernández University of Elche, 03202 Elche, Alicante, Spain;2. Department of Statistics and Operations Research, University of Alicante, 03071 Alicante, Spain |
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Abstract: | 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. |
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Keywords: | Linear programming Semi-infinite programming Ill-posedness |
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