Robust linear optimization under general norms

By Dimitris J. Bertsimas, Dessislava A. Pachamanova, Melvyn Sim. Operations Research Letters, 2004

541 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/d76721a17e5c7a17141fa6b1e9f0d1323e5d4301

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In Control and Systems Engineering

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Citations in the corpus

Robust game theory (2006, result): “Similarly, we have the following lemma, establishing an analogous result for the set of robust-optimization equilibria.”
Deriving robust counterparts of nonlinear uncertain inequalities (2014, unknown): “This result is also obtained in [11] for linear constraints.”
On Robustness and Regularization of Structural Support Vector Machines (2014, methodology): “The result in Theorem 5.1 uses the technique of robust linear programming with arbitrary norms that is introduced in Bertsimas et al. (2004).”
Robust and Data-Driven Optimization: Modern Decision-Making Under Uncertainty (2006, background): “[16] have proposed a robust optimization approach based on polyhedral uncertainty sets, which preserves the class of problems under analysis, e.g., the robust counterpart of a linear programming problem remains a linear programming problem, and thus has advantages in terms of tractability in…”
ON NONSMOOTH OPTIMALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS (2014, background): “Robust optimization, which has emerged as a powerful deterministic approach for studying optimization problems under uncertainty [3, 5, 6, 7], associates with the uncertain program (UP) its robust counterpart [2, 4, 16], (RP) inf{f(x) | gi(x, vi) ≤ 0, ∀vi ∈ Vi, i = 1, .”
A Robust Optimization Perspective on Stochastic Programming (2007, methodology): “Computational tractability of robust linear constraints is achieved by considering tractable uncertainty sets such as ellipsoids (see Ben-Tal and Nemirovski 2000) and polytopes (see Bertsimas and Sim 2004a), which yield robust counterparts that are second-order conic constraints and linear constrain”
Tractable Approximations to Robust Conic Optimization Problems (2006, unknown): “• The l1 ∩ l∞ norm: max{ 1 Γ‖u‖1, ‖u‖∞}, Γ > 0 (see [9, 8] ).”
Distributionally Robust Optimization: A Review (2019, unknown): “[37], Chen et al.”
Theory and Applications of Robust Optimization (2010, methodology): “For instance, when ‖ · ‖ is the Euclidean norm, and x∗ is feasible to the robust problem, Theorem 2 can be shown [23] to imply the guarantee”
Enterprise-wide optimization for industrial demand side management: Fundamentals, advances, and perspectives (2016, background): “Since then, probabilistic guarantees have been derived for a number of different robust formulations (Bertsimas et al., 2004; Bertsimas & Sim, 2006; Chen et al., 2007).”
Constructing Uncertainty Sets for Robust Linear Optimization (2009, background): “Delbaen (2000) shows that CVaR is the smallest upper bound to VaR among all coherent risk measures that depend only on the distribution of the underlying random variable.”