Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications

By Bernardo K. Pagnoncelli, Shabbir Ahmed, Alexander Shapiro. J. Optimization Theory and Applications, 2009

578 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/7542620e28e786fc36f3cbb3cc3807883c676e64

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In Control and Systems Engineering

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Data-driven chance constrained stochastic program (2015, background): “[25]), which are computationally tractable and can guarantee to obtain a solution satisfying a chance constraint with high probability.”
Stochastic Unit Commitment With Uncertain Demand Response (2013, methodology): “Then, the expected value function is replaced with the sample average function, and accordingly the chance constraint is replaced with anMILP reformulation as in [4].”
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 joint chance constraints with second-order moment information (2011, background): “To see that the converse implication holds as well, we note that for any fixed P ∈ P , the mapping γ → P(L(ξ̃) ≤ γ ) is upper semi-continuous, see [21].”
A tractable approximation of non-convex chance constrained optimization with non-Gaussian uncertainties (2015, methodology): “On the other hand, the SAA technique (Pagnoncelli, Ahmed, and Shapiro 2009, Wang and Ahmed 2008, etc.) replaces a chance constraint Pr{g(u, ξ) ≤ 0} by a relative-frequency count of satisfaction of this constraint for samples {ξ 1, . . . , ξN } ⊂ ; i.e. pN (u) = 1 N N∑ k=1 I(−∞,0] ( g(u, ξ k) ) ≥ α,…”
A Chance-Constrained Two-Stage Stochastic Program for Unit Commitment With Uncertain Wind Power Output (2012, methodology): “Following the method described in [15] and [16], we construct a -confidence upper bound on :”