Adjustable robust solutions of uncertain linear programs

By Aharon Ben-Tal, A. Goryashko, E. Guslitzer, Arkadi Nemirovski. Mathematical programming, 2004

1,766 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2a78b294405635b93089806246f33204cc332985

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Citations in the corpus

Self-regularity - a new paradigm for primal-dual interior-point algorithms (2002, background): “The major bulk of the AARC methodology and results as presented in the main body of this chapter originate from [13].”
Distributionally Robust Optimization: A Review (2019, background): “21Restricting the recourse decision function y(ξ) to the class of functions that are affinelydependent on ξ, referred to as linear decision rules, is an approach to derive computationally tractable problems to approximate stochastic programming and robust optimization models [74, 75, 24].”
Robust intermodal hub location under polyhedral demand uncertainty (2016, neutral): “A robust solution is one whose worst case performance over all possible realizations in the uncertainty set is the best (see, e.g., Atamtürk, 2006; Ben-Tal et al., 2004; Ben-Tal and Nemirovski, 1998, 1999, 2008; Bertsimas and Sim, 20 03, 20 04; Mudchanatongsuk et al., 20 08; Ordóñez and Zhao, 2007;…”
A distributional interpretation of robust optimization (2010, neutral): “[4, 7].”
Optimization over state feedback policies for robust control with constraints (2006, methodology): “More recently, it has been revisited as a means for finding solutions to a class of robust optimization problems, called affinely adjustable robust counterpart (AARC) problems [3,11], and robust model predictive control problems [21, 28].”
A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty (2008, methodology): “We follow the robust optimization methodology as introduced by Ben-Tal and Nemirovski (1998, 1999) and ElGhaoui et al. (1998) for linear quadratic and general convex programs, that were subsequently extended to integer programming by Bertsimas and Sim (2003). The general approach of robust optimizat”
Selected topics in robust convex optimization (2007, background): “What we intend to add here, is that the AARC of uncertain LP without fixed recourse admits a tight tractable approximation, provided that the perturbation set ∆Z is the intersection of L ellipsoids centered at 0 [17].”
Evacuation Transportation Planning Under Uncertainty: A Robust Optimization Approach (2009, background): “Proof Note the following relation for any real numbers ui and v (see Ben-Tal et al. (2004) for more details).”
Two-Stage Robust Network Flow and Design Under Demand Uncertainty (2007, background): “[4], in which the au19 thors study two-stage robust linear programming under the name adjustable robust linear 20 programming.”
Class-Weighted Classification: Trade-offs and Robust Approaches (2020, neutral): “Robust optimization is a well-studied topic (Ben-Tal and Nemirovski, 1999, 2003; Ben-Tal et al., 2004, 2009).”
Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach (2005, methodology): “come this difficulty, Ben-Tal et al. (2004) suggested to approximate the ARC solution by restricting these functional relations to be affine.”
Adaptive Distributionally Robust Optimization (2019, methodology): “Dynamic optimization models, where decisions adapt to the uncertain outcomes as they unfold in stages, typically suﬀer from the “curse of dimensionality” and are computationally intractable (see, for instance, Shapiro and Nemirovski 2005, Dyer and Stougie 2006, Ben-Tal et al. 2004).”
Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, neutral): “[9] that (54) takes place if and only if there exists λ0 ≥ 0 such that (α0(z)−λ0)v(2) + 2v ∑”
Robust Optimization (2021, background): “The major bulk of the AARC methodology and results as presented in the main body of this chapter originate from [13].”
MIP Reformulation for Max-Min Problems in Two-Stage Robust SCUC (2017, methodology): “The affine policy (AP) as shown in [17] is successfully adopted in the literature [16], [18]–[20] with better computation performance.”
Predictive Control for Linear and Hybrid Systems (2017, methodology): “Recently, it re-appeared in robust optimization work by Guslitzer and Ben-Tal [136, 46], and in the context of robust MPC in the work of van Hessem & Bosgra, Löfberg and Goulart & Kerrigan [281, 194, 130].”