Robust solutions of Linear Programming problems contaminated with uncertain data

By Aharon Ben-Tal, Arkadi Nemirovski. Mathematical programming, 2000

1,883 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6e5f423442302a3b0988246cea99bac7bc830761

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Citations in the corpus

On Robust Optimization (2015, methodology): “Except for ε-constraint robust OPs, which were just recently introduced in [5], the mentioned concepts are well-known in the literature, see [2, 3, 4, 6, 7].”
Distributionally Robust Optimization: A Review (2019, background): “[100], Ben-Tal and Nemirovski [19], Bertsimas and Sim [34], Ben-Tal and Nemirovski [20], Ben-Tal et al.”
Robust and Data-Driven Optimization: Modern Decision-Making Under Uncertainty (2006, background): “In the mid-1990s, research teams led by Ben-Tal and Nemirovski ([7], [8], [9]) and El-Ghaoui and Lebret ([27], [28]) addressed the issue of overconservatism by restricting the uncertain parameters to belong to ellipsoidal uncertainty sets, which removes the most unlikely outcomes from consideration…”
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, background): “As a promising alternative paradigm, robust optimization does not require accurate knowledge on probability distributions of uncertain parameters [87-89].”
Adaptive Distributionally Robust Optimization (2019, background): “…is described by a distribution free uncertainty set, which is typically a conic representable bounded convex set (see, for instance, El Ghaoui and Lebret 1997, El Ghaoui et al. 1998, Ben-Tal and Nemirovski 1998, 1999, 2000, Bertsimas and Sim 2004, Bertsimas and Brown 2009, Bertsimas et al. 2011).”
Robust Classification (2019, background): “On the other hand, robust solutions for these identical problems, which are feasible for all perturbations up to 0.1%, lead to objective values that are within 1% of the optimal (Ben-Tal and Nemirovski 2000).”
Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty (2012, background): “ X i∈W |ri| γi ≤ Γ ) . (2.49) This set was introduced in [6]. Another candidate is the ellipsoidal set E(A,b) = r ∈ RW : rT Ar ≤ b , (2.50) where A ∈ RW×W is positive-deﬁnite and b ≥ 0 is a real; see [2], [28]. We can now formally proceed as follows: 22 Chance Constrained Optimal Power Flow Deﬁnitio”
Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach (2005, methodology): “Natural choices of ¯ d and S when the demand vector is stochastic are ¯ d = E�d� and S = cov�d� (see Ben-Tal and Nemirovski 2000, 2002 ).”
Data-driven chance constrained stochastic program (2015, background): “, Soyster [37], Ben-Tal and Nemirovski [2], Bertsimas and Sim [3], Calafiore [4] and Ben-Tal et al.”
General Robust-Optimization Formulation for Nonlinear Programming (2007, background): “and are obviously more stringent than the original constraints G ≤ 0. The newly added nonnegative terms in ( 4 ) play the important role of safety margins.”
Robust possibilistic programming for socially responsible supply chain network design: A new approach (2012, background): “Several years later, Ben-Tal and Nemirovski [49,50] and El-Ghaoui et al. [51] put a significant step forward in RP theory by extending the work by Soyster [43] for uncertain linear problems with different convex uncertainty sets.”
A unified approach for different concepts of robustness and stochastic programming via non-linear scalarizing functionals (2013, background): “3) proposed by Ben-Tal and Nemirovski in [30], is defined by”
Selected topics in robust convex optimization (2007, background): “[7,9]), while the set ZII given by (38) is the intersection of the same unit box and the ‖ · ‖1-ball of the radius Ω √ d (“budgeted uncertainty” of Bertsimas and Sim).”
Two-Stage Robust Network Flow and Design Under Demand Uncertainty (2007, background): “Research on robust optimization has recently received renewed attention (Atamtürk 2006; Averbakh 2000, 2001; Ben-Tal and Nemirovski 1998, 2000; Bertsimas and Sim 2003, 2004, 2006; Bertsimas and Thiele 2006; Bienstock and Özbay 2005; Erdo˘ gan and Iyengar 2006; El Ghaoui et al. 1998; Goldfarb and…”
Robust Optimization (2021, methodology): “The analysis of linear optimization problems from the NETLIB collection(1) reported in [7] reveals that for 13 of 94 NETLIB problems, random 0.”
On Robustness and Regularization of Structural Support Vector Machines (2014, background): “In general, robust optimization addresses optimization problems in which some degree of uncertainty governs the known parameters of the model (Ben-Tal & Nemirovski, 1998; 1999; 2000; 2001; Bertsimas & Sim, 2004).”