Stability of Linear Inequality Systems in a Parametric Setting

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

Journal of Optimization Theory and Applications, 2005, vol. 125, issue 2, No 2, 275-297

Abstract: Abstract In this paper, we propose a parametric approach to the stability theory for the solution set of a semi-infinite linear inequality system in the n-dimensional Euclidean space $${\mathbb R}^{n}$$ . The main feature of this approach is that the coefficient perturbations are modeled through the so-called mapping of parametrized systems, which assigns to each parameter, ranging in a metric space, a subset of $${\mathbb R}^{n+1}$$ . Each vector of this image set provides the coefficients of an inequality in $${\mathbb R}^{n}$$ and the whole image set defines the inequality system associated with the parameter. Thus, systems associated with different parameters are not required to have the same number (cardinality) of inequalities. The paper is focused mainly on the structural stability of the feasible set mapping, providing a characterization of the Berge lower-semicontinuity property. The role played by the strong Slater qualification is analyzed in detail.

Keywords: Stability; parametrized systems; linear inequality systems; feasible set mapping (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-004-1838-8

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