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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ALSO-X and ALSO-X+: Better Convex Approximations for Chance Constrained Programs
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References
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Proceedings ArticleDOI
YALMIP : a toolbox for modeling and optimization in MATLAB
TL;DR: Free MATLAB toolbox YALMIP is introduced, developed initially to model SDPs and solve these by interfacing eternal solvers by making development of optimization problems in general, and control oriented SDP problems in particular, extremely simple.
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R. T. Rockafellar,S Uryasev +1 more
TL;DR: In this paper, a new approach to optimize or hedging a portfolio of financial instruments to reduce risk is presented and tested on applications, which focuses on minimizing Conditional Value-at-Risk (CVaR) rather than minimizing Value at Risk (VaR), but portfolios with low CVaR necessarily have low VaR as well.
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.
Journal ArticleDOI
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.
Journal ArticleDOI
The scenario approach to robust control design
TL;DR: A rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial-time solution, if robustness is intended in the proposed risk-adjusted sense.
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