The Price of Robustness

By Dimitris J. Bertsimas, Melvyn Sim. Operational Research, 2004

4,906 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/5c524e6e76f0f6b707e2fe74550bdb7782404616

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

In Ocean Engineering

Citations in the corpus

Robust Regression and Lasso (2008, background): “In that paper, and in most of the subsequent research in this area and the more general area of Robust Optimization (see [12, 13] and references therein) the disturbance is taken to be either row-wise and uncorrelated [14], or given by bounding the Frobenius norm of the disturbance matrix [11].”
Kullback-Leibler divergence constrained distributionally robust optimization (2012, methodology): “Robust optimization (see, for instance, Ben-Tal and Nemirovski (1998, 2000), Bertsimas and Sim (2004), and El Ghaoui et al. (1998)) targets to find an optimal solution that is, to some extent, immune to the ambiguity in the parameters.”
Robust linear optimization under general norms (2004, methodology): “Bertsimas and Sim [7] consider uncertainty sets given by & M(vec( ˜ A) − vec( A)) & p 6 with p ∈ [1; n] and for y ∈ R n×1 & y & p = max {S∪{t}|S⊆N;|S|6p;t∈N \S} ×    j∈S |y j | + (p − −p)|y t |    : The fact that & y & p is indeed a norm, i.e., & y & p ¿ 0, & cy & p = |c| · & y & p , & y & p =”
Strategic facility location, capacity acquisition, and technology choice decisions under demand uncertainty: Robust vs. non-robust optimization approaches (2017, background): “When p = 2, the ellipsoidal uncertainty set is obtained, with its corresponding robustness parameter Ω. Scalars Γ and Ω can be defined in terms of each other, namely Γ = Ω √ n (e.g., Bertsimas and Sim, 2004).”
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).”
Strategic Bidding for a Virtual Power Plant in the Day-Ahead and Real-Time Markets: A Price-Taker Robust Optimization Approach (2016, methodology): “It is worthy to note that the RO models used in this paper could be extended to consider directly correlated uncertain data as proposed in [12].”
Distributionally Robust Co-Optimization of Energy and Reserve Dispatch (2016, background): “The trade-off is usually manually decided through the utilization of a budget constraint [35], which is a 1-norm inequality and controls the total deviation from the forecast by specifying a budget of uncertainty.”
Distributionally Robust Logistic Regression (2015, background): “In contrast, robust optimization ignores all distributional information and aims to minimize the worst-case cost under all possible uncertainty realizations [15, 16, 17].”
Data-driven robust optimization (2013, methodology): “Many approaches ([5, 15, 21]) to constructing uncertainty sets for (1) assume ũ is a random variable whose distribution P∗ is not known except for some assumed structural features.”
A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty (2008, background): “Robust solutions have the potential to be efficient solutions in practice, since they tend not to be far from the optimal solution of the deterministic problem and significantly outperform the deterministic optimal solution in the worst case (Goldfarb and Iyengar, 2003; Bertsimas and Sim, 2004).”
A constrained robust least squares approach for contaminant release history identification (2006, methodology): “[11] RLS has been successfully applied to robust controller analysis [El Ghaoui and Lebret, 1997; De Fonseca et al., 2001], image processing [Schubert, 2003], structural analysis [Ben-Tal and Nemirovski, 1997; Mares et al., 2002], and financial analysis [Bertsimas and Sim, 2004].”
Multiarea Stochastic Unit Commitment for High Wind Penetration in a Transmission Constrained Network (2013, methodology): “(2012) use a robust optimization formulation of the unit commitment problem, where locational demand is assumed to obey the polyhedral and cardinal uncertainty models defined by Bertsimas and Sim (2004). The authors present a Benders’ decomposition algorithm for solving the problem with transmission”
Risk-Based Admissibility Assessment of Wind Generation Integrated into a Bulk Power System (2015, background): “The other is the uncertainty set approach, where a set of inequalities are used to characterize the variation and uncertainty of wind generation, including the upper and lower bounds of uncertainty in each period, the intensity of power fluctuation, and the correlation of forecast errors of differen”
Robust game theory (2006, methodology): “Similarly, we have the following lemma, establishing an analogous result for the set of robust-optimization equilibria.”