On Distributionally Robust Chance-Constrained Linear Programs

By Giuseppe Carlo Calafiore, Laurent El Ghaoui. 2006

524 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/5a0250b8b10532cef298cb203601a53cf0f354e0

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In Control and Systems Engineering

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Citations in the corpus

Data-driven robust optimization (2013, methodology): “Although we focus on [17] and [24] in this paper, this strategy applies equally well to a host of other methods beyond DRO, such as the likelihood estimation approach of [48].”
Data-driven chance constrained stochastic program (2015, background): “, Charnes and Cooper [8], Prékopa [31], and Calafiore and El Ghaoui [7]), and provides conservative convex approximations (see, e.”
Distributionally Robust Markov Decision Processes (2010, background): “, Popescu [26], Delage and Ye [12], Calafiore and El Ghaoui [10], and Goh and Sim [18]).”
Distributionally Robust Chance Constrained Optimal Power Flow with Renewables: A Conic Reformulation (2018, background): “It can be seen that even when the risk parameters are all equal to 0.2, our model is quite robust and the chance that a line or bus capacity will be violated is close to zero for most of distributions.”
Robust SAA (2014, methodology): “As mentioned, in [11, 13], the authors extended DRO to the data-driven setting.”
Distributionally Robust Optimization: A Review (2019, background): “The class of radially-symmetric distributions contains for example Gaussian, truncated Gaussian, uniform distribution on ellipsoidal support, and nonunimodal densities [61]”
Regularization via Mass Transportation (2017, background): “, Calafiore and El Ghaoui [18], Delage and Ye [25], Goh and Sim [35], Wiesemann et al.”
Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, background): “The distance-based approach considers distributions that are close, in the sense of a chosen statistical distance, to a nominal distribution ν , such as an empirical distribution or a Gaussian distribution (El Ghaoui et al. [18], Calaﬁore and El Ghaoui [13]).”
Robust sample average approximation (2014, methodology): “In contrast to SAA, however, themethods of [13,15] do not generally enjoy asymptotic convergence.”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, background): “Even though distributionally robust chance constrained programs with Wasserstein ambiguity sets around the empirical are approximated by) tractable conic programs [16, 21, 48, 115].”
Percentile Optimization for Markov Decision Processes with Parameter Uncertainty (2010, methodology): “Using Theorem 3.1 from Calafiore and El Ghaoui (2006) , Theorem 1 can naturally be extended to this case.”
Distributionally Robust Convex Optimization (2014, unknown): “Robust optimization, ambiguous probability distributions, conic optimization.”
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, methodology): “of all distributions sharing the same known mean and covariance were reformulated as convex second-order cone constraints [118].”
Data-driven risk-averse stochastic optimization with Wasserstein metric (2018, background): “Key words: stochastic optimization; data-driven decision making; Wasserstein metric ∗The basic idea and main results of this paper are also available in [29] and in the first author’s dissertation [27].”