Journal ArticleDOI
Distributionally robust joint chance constraints with second-order moment information
TLDR
It is proved that this approximation is exact for robust individual chance constraints with concave or (not necessarily concave) quadratic constraint functions, and it is demonstrated that the Worst-Case CVaR can be computed efficiently for these classes of constraint functions.Abstract:
We develop tractable semidefinite programming based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove that this approximation is exact for robust individual chance constraints with concave or (not necessarily concave) quadratic constraint functions, and we demonstrate that the Worst-Case CVaR can be computed efficiently for these classes of constraint functions. Next, we study the Worst-Case CVaR approximation for joint chance constraints. This approximation affords intuitive dual interpretations and is provably tighter than two popular benchmark approximations. The tightness depends on a set of scaling parameters, which can be tuned via a sequential convex optimization algorithm. We show that the approximation becomes essentially exact when the scaling parameters are chosen optimally and that the Worst-Case CVaR can be evaluated efficiently if the scaling parameters are kept constant. We evaluate our joint chance constraint approximation in the context of a dynamic water reservoir control problem and numerically demonstrate its superiority over the two benchmark approximations.read more
Citations
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Journal ArticleDOI
Solving linear programs with joint probabilistic constraints with dependent rows using a dynamical neural network
Siham Tassouli,Abdel Lisser +1 more
TL;DR: In this article , a joint probabilistic constrained linear program with dependent rows is studied, where the dependence between the rows is driven by Gumbel-Hougaard copula.
Proceedings Article
Sequential Learning under Probabilistic Constraints
TL;DR: Under a Bayesian framework, this work introduces a scheme that provides statistical feasibility guarantees through the time horizon, by using posterior Monte Carlo samples to form sampled constraints which leverage the scenario generation approach in chance-constrained programming.
Proceedings ArticleDOI
Wasserstein Two-Sided Chance Constraints with An Application to Optimal Power Flow
TL;DR: In this article , a two-sided chance constraint (2-sided CC) is proposed to model the uncertain parameters through a Wasserstein ball centered at a Gaussian distribution and derive a hierarchy of conservative approximations based on second-order conic constraints.
Journal ArticleDOI
A Distributionally Robust Scheduling Approach for Uncertain Steelmaking and Continuous Casting Processes
TL;DR: In this paper , a new model is presented to handle the cast break problem caused by small daily disruptions in the processing time of the steelmaking and continuous casting (SCC) production process, where the exact distribution of the uncertain parameters is unknown, and support set, mean and covariance information is used to describe the uncertain processing time.
Journal ArticleDOI
Computationally Efficient Data-Driven Joint Chance Constraints for Power Systems Scheduling
TL;DR: In this paper , the authors propose a data-driven nonparametric joint chance-constrained programming for multi-interval power system management, where reserve and transmission line constraints are modeled as data driven JCCs and piecewise uniform kernel functions incorporate historical data of uncertain parameters into optimization.
References
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R. T. Rockafellar,S Uryasev +1 more
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Journal ArticleDOI
Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems
Erick Delage,Yinyu Ye +1 more
TL;DR: This paper proposes a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix) and demonstrates that for a wide range of cost functions the associated distributionally robust stochastic program can be solved efficiently.
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Second-order cone programming
Farid Alizadeh,Donald Goldfarb +1 more
TL;DR: SOCP formulations are given for four examples: the convex quadratically constrained quadratic programming (QCQP) problem, problems involving fractional quadRatic functions, and many of the problems presented in the survey paper of Vandenberghe and Boyd as examples of SDPs can in fact be formulated as SOCPs and should be solved as such.
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