Regularity modulus of arbitrarily perturbed linear inequality systems

Calmness modulus of fully perturbed linear programs

This paper provides operative point-based formulas (only involving the nominal data, andnot data in a neighborhood) for computingor estimating the calmness modulus of the optimal set (argmin) mapping in linear optimization under uniqueness of nominal optimal solutions. Our analysis is developed in two different parametric settings. First, in the framework of canonical perturbations (i.e., pertu...

Stability of perturbed linear distributed parameter systems

We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA”. with (Y < 4. The estimate is given in terms of t...

Approximation of singularly perturbed linear hyperbolic systems

This paper is concerned with systems modelled by linear singularly perturbed partial differential equations. More precisely a class of linear systems of conservation laws with a small perturbation parameter is investigated. By setting the perturbation parameter to zero, the full system leads to two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system repre...

Symmetric Linear Systems with Perturbed Input Data

We present a method for constructing a set of inequalities which describe completely the so–called symmetric solution set Ssym := {x ∈ Rn| Ax = b, A = A ∈ [A], b ∈ [b]}. Here, [A] is an n × n interval matrix satisfying [A] = [A] and [b] is an interval vector with n components.

Explicit ABS Solution of a Class of Linear Inequality Systems and LP Problems