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Limit Laws for Empirical Optimal Solutions in Random Linear Programs by Marcel Klatt; Axel Munk; Yoav Zemel is a Engineering article available to read on EtoBox.

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## Abstract We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. For the corresponding random linear program, we characterize under general assumptions the random fluctuations of the empirical optimal solutions around their population quantities after standardization by a distributional limit theorem. Our approach is geometric in nature and further relies on duality and the collection of dual feasible basic solutions. The limiting random variables are driven by the amount of degeneracy inherent in linear programming. In particular, if the corresponding dual linear program is degenerate the asymptotic limit law might not be unique and is determined from the way the empirical optimal solution is chosen. Furthermore, we include consistency and convergence rates of the Hausdorff distance between the empirical and the true optimality sets as well as a limit law for the empirical optimal value involving the set of all dual optimal basic solutions. Our analysis is motivated from statistical optimal transport that is of particular interest here and distributional limit laws for empirical optimal transport plans fo

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Author

Marcel Klatt; Axel Munk; Yoav Zemel

Publisher

Springer Science and Business Media LLC

Published

2022

Language

EN

Field

Engineering (Social Sciences)