Introduction to Stochastic Programming

By A. A. Ayuso, L. F. Bueno, María Celeste Pizarro Romero. 2009

3,232 citations recorded by the source corpus.

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Citations in the corpus

Optimal Distributed Online Prediction Using Mini-Batches (2010, background): “Before continuing, we note that the stochastic online prediction problem is closely re-lated, but not identical, to the stochastic optimization problem (see, e.g., Wets, 1989; Birge and Louveaux, 1997; Nemirovski et al., 2009).”
Scenario Generation of Wind Power Based on Statistical Uncertainty and Variability (2013, background): “In recent years, a number of authors have adopted the stochastic programming approach [8] to make informed decisions for the optimal operation of wind-integrated power systems (WPS) (e.”
On Ensuring that Intelligent Machines Are Well-Behaved (2017, background): “In general, stochastic programming methods allow for many variants of optimization problems wherein there is uncertainty about some of the parameters of the optimization problem [Birge and Louveaux, 2011].”
Stochastic Equilibrium Problems and Stochastic Mathematical Programs with Equilibrium Constraints: A Survey 1 (2009, background): “In stochastic programming [4, 24], two-stage stochastic programming with recourse and chance-constrained programming are, among others, popular vehicles for constructing deterministic models, for which rich theory and many practical algorithms have been developed for half a century.”
Distributionally Robust Optimization and Its Tractable Approximations (2010, methodology): “In the latter, uncertainties are typically modeled as random variables with known distributions and have been used to obtain analytic solutions to important classes of problems (see, e.g., Birge and Louveaux 1997, Ruszczynski and Shapiro 2003).”
The recoverable robust facility location problem (2015, unknown): “[12] J.”
The design of robust value-creating supply chain networks (2010, methodology): “To consider the random variables explicitly in the SCN design model, a proactive stochastic programming (Birge and Louveaux, 1997; Ruszczynski and Shapiro, 2003, Shapiro, 2007) approach must be used.”
Mixed interval–fuzzy two-stage integer programming and its application to flood-diversion planning (2007, unknown): “1981 , Birge and Louveaux 1988 , 1997 , Ruszczynski 1993 ).”
JuMP: A Modeling Language for Mathematical Optimization (2015, background): “This structure has been well studied and arises from stochastic programming [15], contingency analysis [69], multicommodity flow [21], and many other contexts.”
A multi-objective stochastic programming approach for supply chain design considering risk (2008, background): “Due to the stochastic nature of the performance associated with the second-stage decisions, the objective function, traditionally, consists of the sum of the firststage performance measure and the expected secondstage performance; refer to Birge and Louveaux (1997) for more details.”
Stochastic Energy Scheduling in Microgrids With Intermittent Renewable Energy Resources (2014, background): “Details about the classical two-stage or multi-stage stochastic programming can be found in [12].”
Model-Free Renewable Scenario Generation Using Generative Adversarial Networks (2017, unknown): “Despite the tremendous advances recently achieved, scenario generation remains a challenging problem [8], [9].”
Confidence level solutions for stochastic programming (2000, unknown): “Q is bounded and closed convex set, and we can fix some point x0 ∈ Q such that ‖ x− x0 ‖≤ R for all x ∈ Q. 2.”
Adaptive Distributionally Robust Optimization (2019, methodology): “For more information, we refer interested readers to Birge and Louveaux (1997).”
A Robust Optimization Perspective on Stochastic Programming (2007, background): “History : Received December 2004; revisions received June 2005, May 2006; accepted December 2006.”
On stochastic gradient and subgradient methods with adaptive steplength sequences (2011, unknown): “Research by Ermoliev and his coauthors [2]–[5] focused largely on quasigradient (subgradient) methods and considered a host of stochastic programming problems, amongst them being two-period recourse-based problems (see [6]).”
Distributionally Robust Convex Optimization (2014, unknown): “Robust optimization, ambiguous probability distributions, conic optimization.”
Robust Linear Optimization With Recourse (2009, methodology): “(Bertsimas and Tsitsiklis provide an introduction to these techniques in [10]; the reader is also referred to Birge and Louveaux [13] and Kall and Wallace [25] for an extensive treatment of these methods in the context of stochastic optimization.)”