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Milan Hladík
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Milan Hladík: Charles University

Chapter Chapter 9 in Interval Linear Programming and Extensions, 2025, pp 189-234 from Springer

Abstract: Abstract In addition to optimal values and optimal solutions, other issues are studied in interval linear programming. First, we introduce duality and examine under which conditions the duality gap is zero for each or for at least one realization of the interval coefficients. Next, we analyze transformations of the constraints, such as splitting equations into double inequalities or introducing slack variables; these techniques are common in LP. However, in the interval case, they might cause dependencies, and thus, they are no more equivalent. Other issues we address are (un)boundedness and optimality for all or for at least one realization; the maximum (worst-case) optimal value, considering only finite cases; and redundancy of the constraints.

Date: 2025
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DOI: 10.1007/978-3-031-85096-7_9

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