The empirical behavior of sampling methods for stochastic programming

By Jeff T. Linderoth, Alexander Shapiro, Stephen J. Wright. Annals of Operations Research, 2006

488 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/898ebc2de8b4553b7e3eb06091bf0abccc1c14ad

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In Control and Systems Engineering

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Citations in the corpus

Bayesian Hierarchical Modeling for Integrating Low-Accuracy and High-Accuracy Experiments (2008, unknown): “From the assumption that ρ(·), δ(·) and (·) are independent of yl in (7), the distributions of the numerator and the denominator in (15) are as follows: p(yh[x0),yh|yl,θ1,θ2,θ3] ∼ N(ρ0y l1 + δ01n1+1, σ 2 ρW ∗ ρ + σ 2 δR ∗ δ + σ 2 I(n1+1)×(n1+1)), p(yh|yl,θ1,θ2,θ3) ∼ N(ρ0yl1 + δ01n1 , σ(2) ρWρ + σ(2)”
On stochastic gradient and subgradient methods with adaptive steplength sequences (2011, unknown): “This approach relies on using a sample from the underlying distribution to construct a deterministic sample-average problem, which can be subsequently solved via standard nonlinear programming solvers, as seen in [19].”
An optimal method for stochastic composite optimization (2011, methodology): “Recent theoretical studies (cf., [16,45,46]) and numerical experiments (see e.g., [23,27,51]) show that the SAA method coupled with a good (deterministic) algorithm could be reasonably efﬁcient for solving certain classes of two stage stochastic programming problems.”
Dealing with asynchronicity in parallel Gaussian Process based global optimization (2010, methodology): “Numerical experiments with the SAA method are reported in [50, 51, 83], for example.”
Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal scheduling (2011, methodology): “The LHS method has been successfully used in stochastic optimization problems of the form minx∈X{g(x) := E[G(x, ζ )]}, see for instance [1, 20 , 38].”
Evaluation of scenario-generation methods for stochastic programming (2007, methodology): “A similar method, together with computational results, can be found in [13].”
Optimization of Resource Provisioning Cost in Cloud Computing (2012, unknown): “Ç”
Robust Stochastic Approximation Approach to Stochastic Programming (2008, methodology): “Recent theoretical studies (cf. [ 11, 25, 26]) and numerical experiments (see, e.g., [12, 13, 29]) show that the SAA method coupled with a good (deterministic) algorithm could be reasonably eﬃcient for solving certain classes of two-stage stochastic programming problems.”
A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs (2019, background): “2SIP is studied extensively in the literature [4, 7, 11, 13–15, 17–20, 24] owing to its applicability in various decision making situations with uncertainty, like the stochastic unit-commitment problems for electricity generation [18, 19], ar X iv :1 91 2.”
Validation analysis of mirror descent stochastic approximation method (2012, methodology): “, [5,6,17]) show that the SAA method coupled with a good deterministic algorithm for minimizing the constructed SAA problem could be reasonably efficient for solving certain classes of SP problems.”
Task-based End-to-end Model Learning in Stochastic Optimization (2017, methodology): “In cases where the underlying probability distribution is known but the objective cannot be solved analytically, it is common to use Monte Carlo sample average approximation methods, which draw multiple iid samples from the underlying probability distribution and then use deterministic optimization ”
Task-based End-to-end Model Learning (2017, unknown): “…distribution is known but the objective cannot be solved analytically, it is common to use Monte Carlo sample average approximation methods, which draw multiple iid samples from the underlying probability distribution and then use deterministic optimization methods (Linderoth et al., 2006).”
Reliability constrained multi-area adequacy planning using stochastic programming with sample-average approximations (2008, methodology): “There are two fundamental approaches to apply sampling techniques; interior [14], [17] and exterior [ 1 ], [8].”
Electric vehicle fleet management in smart grids: A review of services, optimization and control aspects (2016, methodology): “A sample average approximation method [90] is applied to formulate the random inputs and the lower bound estimate principle is used to estimate the optimal value.”
Monte Carlo sampling-based methods for stochastic optimization (2014, unknown): “[152] who also present extensive computational results.”
Optimization under uncertainty: state-of-the-art and opportunities (2004, background): “Impressive computational results on a computational grid are reported by Linderoth, Shapiro, and Wright (2002) on stochastic linear programs with up to 10 81 scenarios .”
Convex optimization under inexact first-order information (2009, methodology): “, [36, 40, 74]) show that the SAA method coupled with a good (deterministic) algorithm could be reasonably efficient for solving certain classes of two stage stochastic programming problems.”