The Unbounded Parametric Tolerable Solution Set
We consider a linear algebraic system A(p)x=b(q), where the elements of the matrix and the right-hand side vector are linear functions of uncertain parameters p, q varying within given intervals [p], [q].В В The so-called parametric tolerable solution set is studied for unboundedness.
В Basing on a characterization of the parametric tolerable solution set as a convex polyhedron, we present necessary and sufficient conditions (in both general and computable forms) for a nonempty parametric tolerable solution set to be unbounded. Every parametric tolerable solution set is represented as a sum of a linear subspace and a bounded convex polyhedron. The latter implies better estimations (outer and inner) for the unbounded parametric tolerable solution set. Numerical examples illustrate the discussed methodology and the solution sets.
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