Distributionally robust joint chance constraints with second-order moment information

By Steve Zymler, D. Kühn, Berç Rustem. Mathematical programming, 2011

671 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/2e3237509325b2de13a9d7785e006dd82e5d483d

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Citations in the corpus

Distributionally Robust Optimization: A Review (2019, background): “[345] study a safe approximation to distributionally robust individual and joint chance constraints based on the worst-case CVaR.”
Data-Driven DG Capacity Assessment Method for Active Distribution Networks (2017, methodology): “6 in [24], this conversion is exact if the scaling vector λ = [λ1 , · · · , λK ] is introduced and treated as decision variables.”
Distributionally Robust Convex Optimization (2014, neutral): “Robust optimization, ambiguous probability distributions, conic optimization.”
Data-driven chance constrained stochastic program (2015, background): “To address these drawbacks, stochastic programs with distributionally robust (or ambiguous) chance constraints (DCCs) are proposed (see, e.g., [2,8,15,16,32,44,48,49], and [19] 1 ).”
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, background): “approximation for distributionally robust joint chance constraints was studied assuming first and second moment [131], and the resulting conservative approximation can be cast as semidefinite program.”
Multi-stage distributionally robust optimization with risk aversion (2021, background): “[49] studied distributionally robust joint chance constraints with second-order moment information.”
Distributionally Robust Solution to the Reserve Scheduling Problem With Partial Information of Wind Power (2015, methodology): “However, it should be emphasized that the sequential convex algorithm cannot guarantee the solution to be the global optimum due to the nonconvexity of the BMI-P [4].”
Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, background): “The moment-based approach considers distributions whose moments (such as mean and covariance) satisfy certain conditions (Scarf et al. [38], Delage and Ye [16], Popescu [35], Zymler et al. [51]).”
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].”
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].”
Outlier detection using distributionally robust optimization under the Wasserstein metric (2017, background): “he way in which Pis dened. One is through a moment ambiguity set, which contains all distributions that satisfy certain moment constraints [see Popescu, 2007, Delage and Ye, 2010, Goh and Sim, 2010, Zymler et al., 2013, Wiesemann et al., 2014]. In many cases it leads to a tractable DRO problem but h”
A tractable approximation of non-convex chance constrained optimization with non-Gaussian uncertainties (2015, background): “Some classes of chance constrained or robust optimization problems can also be modelled as semi-definite optimization problems, e.g. Bertsimas, David, and Caramanis (2011), Feng, Dabbene, and Lagoa (2011), Jasour and Lagoa (2012), Zymler, Kuhn, and Rustem (2013), etc.”
Distributionally Robust Chance Constrained Optimal Power Flow with Renewables: A Conic Reformulation (2018, methodology): “Thus, to overcome the difficulties from these two approaches, here we adopt a distributionally robust chance constrained approach, which allows violation of uncertain constraints with a small probability for a large class of probability distributions and could be reformulated as a tractable convex p”