Robust optimization – methodology and applications

By Aharon Ben-Tal, Arkadi Nemirovski. Mathematical programming, 2002

1,530 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ed28314ca308ce0b39a0eb0a18b65aade38ee4b6

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Citations in the corpus

A modified Benders decomposition method for efficient robust optimization under interval uncertainty (2011, background): “…problem is available in Gabriel et al. (2009). linear objective function in the problem as reported in the literature (e.g., Balling et al. 1986; Ben-Tal and Nemirovski 2002; Bertsimas and Sim 2006; Soyster 1973) or quadratic (e.g., Li et al. 2010) as well as other versions involving convex…”
Ambiguity in portfolio selection (2007, background): “Recall the definition of a robust optimization problem (see Ben-Tal and Nemirovski 2002): If a deterministic optimization problem Maximize (in xÞ : fðx, Þ subject to fiðx, Þ 0, i ¼ 1, . . . , k: ð4Þ contains some parameters and the decision maker only knows some range Z of these parameters, he/she…”
Extreme structural response analysis of truss structures under material uncertainty via linear mixed 0–1 programming (2008, positive): “Using the same uncertainty model, Ben-Tal and Nemirovski [9] developed a unified approach of robust design for a broader class of convex optimization problems.”
Convex Approximations of Chance Constrained Programs (2006, background): “As it could be expected, in the situation in question, Bernstein approximation recovers the robust counterpart (RC) of the original uncertain problem [3], which in our case is the semi-infinite optimization program:”
Selected topics in robust convex optimization (2007, neutral): “Ben-Tal at XVII ISMP, Atlanta, 2000, see [13].”
Enterprise-wide optimization for industrial demand side management: Fundamentals, advances, and perspectives (2016, methodology): “Generalized Benders decomposition (Geoffrion, 1972) and outer approximation (Duran & Grossmann, 1986) have been applied to solve the problem. Since the MINLP is convex in the continuous variables, both solution algorithms are guaranteed to obtain the global optimal solution; however, they require co”
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].”
Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system (2011, neutral): “[18, 19, 20, 21] or Chapter 16-21 in [22]).”
General Robust-Optimization Formulation for Nonlinear Programming (2007, background): “It will be necessary to assume that the inequality constraints in ( 7 ) are strictly satisfiable; i.e., there exists a pair (u, s) ∈ R N”
Evacuation Transportation Planning Under Uncertainty: A Robust Optimization Approach (2009, background): “These papers make a significant step forward and propose less conservative models by considering tractable robust counterparts for nominal problems (Ben-Tal and Nemirovski 2002).”