Distance to Ill-Posedness in Linear Optimization via the Fenchel-Legendre Conjugate

M. J. Cánovas, M. A. López, J. Parra and F. J. Toledo
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M. J. Cánovas: Miguel Hernández University of Elche, Elche
M. A. López: University of Alicante
J. Parra: Miguel Hernández University of Elche, Elche
F. J. Toledo: Miguel Hernández University of Elche, Elche

Journal of Optimization Theory and Applications, 2006, vol. 130, issue 2, No 2, 173-183

Abstract: Abstract We consider the parameter space of all the linear inequality systems, in the n-dimensional Euclidean space and with a fixed index set, endowed with the topology of the uniform convergence of the coefficient vectors. A system is ill-posed with respect to the consistency when arbitrarily small perturbations yield both consistent and inconsistent systems. In this paper, we establish a formula for measuring the distance from the nominal system to the set of ill-posed systems. To this aim, we use the Fenchel-Legendre conjugation theory and prove a refinement of the formula in Ref. 1 for the distance from any point to the boundary of a convex set.

Keywords: Fenchel-Legendre conjugate; stability; well-posedness; linear inequality systems; distance to ill-posedness (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-006-9097-5

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