Ambiguous chance constrained problems and robust optimization

By Emre Erdogan, Garud N. Iyengar. Mathematical programming, 2006

363 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d7a1b94c5b580519f9f9164ad39f3d77c50cca96

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In Management Science and Operations Research

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Citations in the corpus

Two-Stage Robust Network Flow and Design Under Demand Uncertainty (2007, background): “…Averbakh 2000, 2001; Ben-Tal and Nemirovski 1998, 2000; Bertsimas and Sim 2003, 2004, 2006; Bertsimas and Thiele 2006; Bienstock and Özbay 2005; Erdoğan and Iyengar 2006; El Ghaoui et al. 1998; Goldfarb and Iyengar 2003; Kouvelis and Yu 1997; Lim and Shanthikumar 2007; Ordóñez and Zhao 2004,…”
The Stochastic Vehicle Routing Problem for Minimum Unmet Demand (2009, neutral): “the link between the chance-constrained technique and robust optimization [32, 12, 19, 14].”
Preventing undesirable behavior of intelligent machines (2019, background): “For example, ambiguous chance constrained programs allow the distribution, P , of Wi to be unknown, as long as it is within some set of possible distributions P that is known [78].”
Convex Approximations of Chance Constrained Programs (2006, background): “When applied to chance constraints, such worst-case-distribution problems are called ambiguous chance constrained problems (see [14] and references therein).”
Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, neutral): “Then problem (41) is maxx ∫ x−1(1)[−c+λf(t)]dt, with optimal control x∗(t) = 1{λf(t)>c}.”
Kullback-Leibler divergence constrained distributionally robust optimization (2012, background): “Note that such problems are also called ambiguous CCPs in the literature (e.g., Erdogan and Iyengar 2006 and Nemirovski and Shapiro 2006).”
Data-driven chance constrained stochastic program (2015, neutral): “Key words: stochastic optimization; chance constraints; semi-infinite programming; S-Lemma”
Data-driven risk-averse stochastic optimization with Wasserstein metric (2018, neutral): “, D0 1 = {P̂ ∈ M+ : EP̂[ξ] = μ0,EP̂[ξξ >] = μ0μ > 0 + Σ0}, in [12], [14], [8], [23], [30], and [31], among others.”
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, neutral): “approximated by using robust sampled problem [143].”
Distributionally Robust Optimization: A Review (2019, background): “Given this setup, Goldfarb and Iyengar [122] study a DRO approach to different portfolio optimization problems for the return ξ̃ > x on the portfolio x, where ∑n i=1 xi = 1.”
On Ensuring that Intelligent Machines Are Well-Behaved (2017, background): “For example, ambiguous chance constrained programs allow the distribution, P , of Wi to be unknown, as long as it is within some set of possible distributions, P, that is known [Erdoğan and Iyengar, 2006].”
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality (2011, neutral): “[24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], and sample-based optimization has also been used in connection of various application domains, see e.”
Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty (2012, background): “d to be insensitive to data errors. This approach puts CC-OPF within the scope of robust optimization; to be more precise we will be solving an ambiguous chance-constrained problem in the language of [25]. We will write each µi in the form ¯µi + ri, where the ¯µi are point estimates of the µi and th”
From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization (2010, methodology): “Indeed, sampling approximation of the chance constrained problem has been studied theoretically in Calafiore and Campi [11, 12], Ergodan and Iyengar [17] and Luedtke and Ahmed [22].”
Wasserstein Distributional Robustness and Regularization in Statistical Learning (2017, background): “…of the statistical distance include φ -divergences (Ben-Tal et al. 2013, Jiang and Guan 2015, Bayraksan and Love 2015, Wang et al. 2016), Prokhorov metric (Erdo˘gan and Iyengar 2006), and Wasserstein distances (Wozabal 2014, Blanchet and Murthy 2016, Gao and Kleywegt 2016, Esfahani and Kuhn 2017).”
Distributionally Robust Logistic Regression (2015, background): “However, ambiguity sets can also be constructed via distance measures in the spa c of probability distributions such as the Prohorov metric [21] or the Kullback-Leibler divergenc [22].”
Quantifying Distributional Model Risk via Optimal Transport (2016, neutral): “based uncertainty sets, [26,32,41,38,33,9,55,34,29,8] for QUANTIFYING MODEL RISK 25 KL-divergence and other likelihood based uncertainty sets, [42,58,20] for Wasserstein distance based neighborhoods, [19] for neighborhoods based on Prokhorov metric, [6,5] for uncertainty sets based on statistical te”
Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations (2015, methodology): “The models proposed in this paper fall within the scope of data-driven distributionally robust optimization [7,16,20,23].”