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General Interval Linear Systems

In: Interval Linear Programming and Extensions

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  • Milan Hladík

    (Charles University)

Abstract

In this chapter, we consider the general form of linear systems with interval coefficients. First, we focus on linear inequalities and then extend the results to mixed equations and inequalities. For these systems, we introduce weak solutions (solving at least one realization of the interval entries) and discuss the characterization and the geometric shape of the solution set. As another concept, we define strong solvability (solvability of each realization of interval entries) and strong solutions (solving each realization). Again, we characterize these concepts and analyze computational complexity.

Suggested Citation

  • Milan Hladík, 2025. "General Interval Linear Systems," Springer Optimization and Its Applications, in: Interval Linear Programming and Extensions, chapter 0, pages 75-102, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-85096-7_4
    DOI: 10.1007/978-3-031-85096-7_4
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