AE solutions and AE solvability to general interval linear systems
Milan Hlad\'ik
TL;DR
This paper investigates AE solutions and AE solvability in general interval linear systems, providing explicit descriptions, complexity analysis, and conditions for solvability and solutions, including a complete characterization for certain subclasses.
Contribution
It introduces explicit descriptions of AE solutions, analyzes complexity, and offers conditions and characterizations for AE solvability in interval linear systems.
Findings
Explicit description of AE solutions
Complexity analysis of AE solvability
Conditions for equivalence of AE solvability and solutions
Abstract
We consider linear systems of equations and inequalities with coefficients varying inside given intervals. We define their solutions (so called AE solutions) and solvability (so called AE solvability) by using forall-exists quantification of interval parameters. We present an explicit description of the AE solutions, and discuss complexity issues as well. For AE solvability, we propose a sufficient condition only, but for a specific sub-class of problems, a complete characterization is developed. Moreover, we investigate inequality systems for which AE solvability is equivalent to existence of an AE solution.
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