AE Interval Linear Programming

Milan Hladík
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Milan Hladík: Charles University

Chapter Chapter 15 in Interval Linear Programming and Extensions, 2025, pp 455-475 from Springer

Abstract: Abstract In the preceding chapters, we often associated interval parameters with either the universal or the existential quantifier: Some LP property should be satisfied for all or for at least one realization of interval coefficients. In this chapter, we introduce ∀ ∃ $$\forall \exists $$ -quantification, which generalizes both cases. First, we consider ∀ ∃ $$\forall \exists $$ -quantified interval systems of linear equations and inequalities, and we study the corresponding ∀ ∃ $$\forall \exists $$ solutions and solvability. Then, we investigate ∀ ∃ $$\forall \exists $$ -quantified LP problems, for which we propose two robust optimization approaches.

Date: 2025
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DOI: 10.1007/978-3-031-85096-7_15

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