Scenario Approximations of Chance Constraints

By Arkadi Nemirovski, Alexander Shapiro. 2006

240 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/49a0e4add1eab86ab90393959f654fffb1f52257

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In Computer Networks and Communications

In Statistics and Probability

Citations in the corpus

Robust Optimization (2021, background): “2 was announced in [59]; the proof, heavily exploiting the result of Borell [25], was published in [61].”
A tractable approximation of non-convex chance constrained optimization with non-Gaussian uncertainties (2015, methodology): “In addition, instead of designing a tighter approximation for E[h(x, ξ)] by taking infimum with respect to τ (cf. Nemirovski and Shapiro 2006a), a monotonic reduction of (τ , u, s) is computationally much more preferable.”
The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs (2008, methodology): “To circumvent this computational issue, recently, methodologies relying on the randomization over the set of constraints have been introduced [11, 5, 20, 6, 13].”
Ambiguous chance constrained problems and robust optimization (2006, background): “Nemirovski and Shapiro [ 34 ] showed that when Q0 is symmetric with a concentration of measure property and f(x; h) is bi-ane, the set Y[N] contains, with a high probability, a slightly more conservative version of the chance constrained”
Data-driven chance constrained stochastic program (2015, background): “More recently, to solve chance constrained stochastic programs, scenario approximation approaches (see, e.g., [7,28,31], and [33]) are studied and demonstrated to be computationally tractable and can guarantee to obtain a solution satisfying a chance constraint with high probability.”
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality (2011, unknown): “[24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], and sample-based optimization has also been used in connection of various application domains, see e.”
Distributionally Robust Optimization: A Review (2019, background): “(Shapiro [289, Definition 2.1]) A (real-valued) risk measure ρ : Z 7→ R is called law invariant if for all Z,Z ′ ∈ Z, Z d∼ Z ′ implies that ρ(Z) = ρ(Z ′).”
Convex Approximations of Chance Constrained Programs (2006, background): “, uniform in a box, or on the vertices of a box, or normal [19].”
Constructing Uncertainty Sets for Robust Linear Optimization (2009, background): “1For some more recent work using samples in the context of chance-constrainted optimization, see, e.g., Calafiore and Campi [9] and Nemirovski and Shapiro [26].”