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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Bibliographic Details
Published in:Optimization letters Vol. 14; no. 7; pp. 1627 - 1642
Main Author: Ghate, Archis
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020
Subjects:
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
Online Access:Get full text
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Summary: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