A Sample Approximation Approach for Optimization with Probabilistic Constraints

By James R. Luedtke, Shabbir Ahmed. SIAM Journal on Optimization, 2008

694 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/5f0a01bfdd36c1267a8e0b1265ebd55900215ddf

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Citations in the corpus

An integer programming approach for linear programs with probabilistic constraints (2007, background): “Indeed, it has been shown that by solving such a sample approximation it is possible to obtain feasible solutions and lower bounds for PCLP with general distributions, and that the required sample size is polynomial in 1/ǫ [18].”
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, background): “In light of these computational challenges, a large body of related literature is devoted into the development of solution algorithms for chance constrained optimization problems, such as sample average approximation [68], sequential approximation [69], and convex conservative approximation schemes ”
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality (2011, background): “A result similar to (ii) has also been independently established in [41].”
Distributionally robust joint chance constraints with second-order moment information (2011, background): “Recently, Calafiore and Campi [5] as well as Luedtke and Ahmed [17] have proposed to replace the chance constraint (2) by a pointwise constraint that must hold at a finite number of sample points drawn randomly from the distribution Q.”
Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications (2009, methodology): “In [11], the authors applied the same technique to generate bounds on probabilistic versions of the set cover problem and the transportation problem.”
Data-driven chance constrained stochastic program (2015, methodology): “It follows that Remark 3 Luedtke and Ahmed [28] observed that feasible solutions to chance constraint } can be obtained with a higher conﬁdence level if a sample average approximation of the chance constrained problem is solved with the risk level α replaced by a decreased one α (cid:15) ≤ α .”
Distributionally Robust Optimization: A Review (2019, background): “For other research in chance-constrained optimization problem, we refer to Xie et al. [324], Xie and Ahmed [321].”
Lectures on Stochastic Programming: Modeling and Theory (2009, methodology): “For some numerical experiments with these bounds see Luedtke and Ahmed [147].”
A Guide to Sample Average Approximation (2015, methodology): “The sample size directive given by Theorem 15, while useful in some SAA settings, can be overly conservative [Luedtke and Ahmed, 2008, Ruszczy´nski and Shapiro, 2003], often resulting in a loss in computational efficiency.”
Monte Carlo sampling-based methods for stochastic optimization (2014, background): “Luedtke and Ahmed [156] show that, under similar assumptions to those discussed earlier—such as compactness of X and Lipschitz continuity of H with respect to x, or finiteness of X—an exponential convergence of the type (39) holds in this setting as well. consistency with the notation used throughou”
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].”
Constrained Learning With Non-Convex Losses (2021, background): “Indeed, classical learning theory is concerned with unconstrained learning problems [3]–[5] and results for general constrained stochastic programs are often asymptotic, involving a myriad of distributional assumptions [43], [44], [46]–[50].”
Distributionally Robust Chance Constrained Optimal Power Flow with Renewables: A Conic Reformulation (2018, background): “Robust optimization is often too conservative [30], while chance constrained programming is less conservative but is often NP-hard [31], [32].”