Robust continuous linear programs

Continuous linear programs (CLPs) arise in applications such as production/economic planning, continuous-time network flow problems, fluid relaxations of multiclass queueing networks, and control. To the best of the author’s knowledge, this paper proposes the first robust optimization framework for...

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Vydáno v:Optimization letters Ročník 14; číslo 7; s. 1627 - 1642
Hlavní autor: Ghate, Archis
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020
Témata:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Parametric uncertainty
Linear programming duality
Infinite-dimensional optimization
ISSN:1862-4472, 1862-4480
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Popis
Shrnutí:Continuous linear programs (CLPs) arise in applications such as production/economic planning, continuous-time network flow problems, fluid relaxations of multiclass queueing networks, and control. To the best of the author’s knowledge, this paper proposes the first robust optimization framework for CLPs. The main result of the paper is that the robust counterpart of a CLP is also a CLP. Thus, any computational method for the original problem can be applied to the robust problem. For instance, a recent polynomial-time approximation algorithm applies. Further, if the original problem possesses a so-called separable structure, then the robust problem is also separable. Then existing Simplex-type and other discretization-based solution methods can be applied to the robust problem. The paper also provides a bound on the probability that an optimal solution to the robust counterpart violates a constraint in the original problem. Qualitative properties of this bound are discussed and compared with similar bounds for robust finite-dimensional linear programs.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-020-01539-6