Intervalové lineární programování

Garajová, Elif

Interval linear programming provides a modern approach for handling optimization problems affected by various sources of interval-valued uncertainty. Given lower and upper bounds on the inexact data, the model represents a set of linear programs with coefficients that can be independently perturbed within the respective ranges. The thesis forms a systematic study of the optimality properties of interval linear programs and their solutions. Building on the existing research, we present a compilation of results published by the author, which fill in some of the gaps in the state-of-the-art literature on interval programming. We first examine the effects of standard transformations used in linear programming on the optimal solutions and optimal values of interval programs. Then, we characterize the properties of feasibility, optimality and (un)boundedness in the weak and in the strong sense (i.e. whether a property holds for some or for each scenario) and we analyze computational complexity of the associated decision problems. Further, we focus on the optimal solutions and prove that several related decision problems are (co)NP-hard even for interval programs with a fixed constraint matrix. We also show an integer programming reformulation useful in computing the optimal value range and discuss other concepts...

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