Robust solutions of uncertain linear programs
Aharon Ben-Tal,Arkadi Nemirovski +1 more
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TLDR
It is shown that the RC of an LP with ellipsoidal uncertainty set is computationally tractable, since it leads to a conic quadratic program, which can be solved in polynomial time.About:
This article is published in Operations Research Letters.The article was published on 1999-08-01 and is currently open access. It has received 1809 citations till now. The article focuses on the topics: Uncertain data & Linear programming.read more
Citations
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Robust hub network design problem
TL;DR: In this article, a robust formulation for the uncapacitated single and multiple allocation hub location problem where demand is uncertain and its distribution is not fully specified is presented, where a robust model is formulated as a mixed integer nonlinear program and then transformed into a mixed-integer conic quadratic program.
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Robust Corrective Control Measures in Power Systems With Dynamic Line Rating
Matthias Bucher,Göran Andersson +1 more
TL;DR: How DLR can be integrated in a dispatch optimization while managing possible errors in the forecasts of the line ratings with two different approaches is demonstrated and the reduction of overall operational costs is investigated exemplarily as a function of the forecast accuracy.
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Robust Multi-period Fleet Allocation Models for Bike-Sharing Systems
TL;DR: In this article, a time-space network is constructed to describe time-dependent bike flows in the system, and a bike fleet allocation model that considers average historical demand and fixed fleet size is established based on the time space network.
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Real-time management of berth allocation with stochastic arrival and handling times
TL;DR: Results indicate that the proposed reactive approaches can significantly reduce the total realized cost of berthing the vessels as compared to the ongoing practice at the port.
Posted Content
Robust Optimal Control with Adjustable Uncertainty Sets
TL;DR: In this article, a unified framework for constrained robust optimal control problems with adjustable uncertainty sets is developed, where the uncertainty sets are treated as additional decision variables and the problem of determining the optimal size and shape of the uncertainty set is formulated as a tractable convex optimization problem.
References
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Book
Robust and Optimal Control
TL;DR: This paper reviewed the history of the relationship between robust control and optimal control and H-infinity theory and concluded that robust control has become thoroughly mainstream, and robust control methods permeate robust control theory.
BookDOI
Introduction to Stochastic Programming
John R. Birge,Franois Louveaux +1 more
TL;DR: This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.
Book
Interior-Point Polynomial Algorithms in Convex Programming
TL;DR: This book describes the first unified theory of polynomial-time interior-point methods, and describes several of the new algorithms described, e.g., the projective method, which have been implemented, tested on "real world" problems, and found to be extremely efficient in practice.
Journal ArticleDOI
Robust Convex Optimization
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: If U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
Related Papers (5)
Robust solutions of Linear Programming problems contaminated with uncertain data
Aharon Ben-Tal,Arkadi Nemirovski +1 more