Abstract
We are concerned with finite linear constraint systems in a parametric framework where the right-hand side is an affine function of the perturbation parameter. Such structured perturbations provide a unified framework for different parametric models in the literature, as block, directional and/or partial perturbations of both inequalities and equalities. We extend some recent results about calmness of the feasible set mapping and provide an application to the convergence of a certain path-following algorithmic scheme. We underline the fact that our formula for the calmness modulus depends only on the nominal data, which makes it computable in practice.
Highlights
Introduction and OverviewThe present paper deals with parameterized linear inequality systems in Rn of the form at x ≤ qt + pt b, t ∈ T := {1, . . . , m}, (1) C
Where x ∈ Rn is the vector of decision variables regarded as a column vector (i.e. Rn ≡ Rn×1), the prime stands for transposition, at ∈ Rn, pt ∈ Rk and qt ∈ R are given for each index t ∈ T, and b ∈ Rk is the parameter to be perturbed around a nominal element b
For some particular choices of matrix P we succeed to provide point-based expressions for the aimed modulus. This is the case of model (4), which plays a remarkable role in this work because of its application to Section 4, and we point out that the results of this paper extend the calmness analysis developed in [6, 11], as far as it includes inequalities, and equalities
Summary
The present paper deals with parameterized linear inequality systems in Rn of the form at x ≤ qt + pt b, t ∈ T := {1, . . . , m} ,. For some particular choices of matrix P we succeed to provide point-based expressions (depending exclusively on the nominal data) for the aimed modulus This is the case of model (4), which plays a remarkable role in this work because of its application to Section 4, and we point out that the results of this paper extend the calmness analysis developed in [6, 11], as far as it includes inequalities, and equalities.
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