Lectures on Stochastic Programming: Modeling and Theory

By Alexander Shapiro, Darinka Dentcheva †, Andrzej Ruszczynski. 2009

3,105 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Mathematical Optimization

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Citations in the corpus

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information (2018, methodology): “We select the method of SAA (see, e.g., Kim et al., 2015, Shapiro et al., 2009, p. 155) in view of its position as a de facto standard in approximate stochastic programming: it is broadly applicable, commonly used, based on simple principles and supported by an abundant knowledge of its properties,…”
Learning with Pseudo-Ensembles (2014, background): “For example, the optimization community has produced a large body of theoretical and empirical work addressing “stochastic programming” [18] and “robust optimization” [4].”
GradientDICE: Rethinking Generalized Offline Estimation of Stationary Values (2020, methodology): “…address a double sampling issue, Zhang et al. (2020) , where φ ∗ is the Fenchel conjugate of φ , and use the interchangeability principle for interchanging maximization and expectation (Shapiro et al., 2014; Dai et al., 2016), yielding the following problem, which is equivalent to (2): where Here”
DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections (2019, neutral): “By the interchangeability principle [6, 34, 36], we may replace the inner max over scalar ζ to a max over functions ζ : S ×A→ R and obtain a min-max saddle-point optimization:”
Variance-based Regularization with Convex Objectives (2016, background): “3 Fast Rates In cases in which the risk R has curvature, empirical risk minimization often enjoys faster rates of convergence [6, 21].”
Optimization with Sparsity-Inducing Penalties (2011, methodology): “). Finally, from a broader outlook, our—a priori deterministic—optimization problem (1.1) may also be tackled with stochastic optimization approaches, which has been the focus of much recent research [21, 23, 108, 129]. 61 Chapter 10 Conclusions We presented and compared four families of algorithms ”
Optimal randomized classification trees (2021, background): “The estimator θ̂N of the parameter θ is said to be consistent, in the sense of [53], if θ̂N converges with probability 1 (w.”
A Sufficient Condition for Convergences of Adam and RMSProp (2018, background): “Introduction Large-scale non-convex stochastic optimization [23, 5], covering a slew of applications in statistics and machine learning [14, 5] such as learning a latent variable from massive data whose probability density distribution is unknown, takes the following generic formulation: min x∈Rd f(”
Learning Models with Uniform Performance via Distributionally Robust Optimization (2018, background): “1 An extensive literature on coherent risk measures defines utility functions that exhibit “sensible” tail risk preference [7, 75, 58, 85]; there is a duality between distributionally robust optimization and coherent risk measures [e.”
A Guide to Sample Average Approximation (2015, methodology): “When the sample functions are convex, the set of regularity conditions in Theorem 9 can be relaxed by using the theory of epi-convergence [Shapiro et al., 2009, Theorem 5.4].”
Handbook of Simulation Optimization (2014, methodology): “Instead of finding the alternative with the best mean, Trailovic and Pao [57] develop an OCBA approach for finding an alternative with minimum variance.”
Stochastic (Approximate) Proximal Point Methods: Convergence, Optimality, and Adaptivity (2018, positive): “ntly and identically distributed from P and uses these samples to minimize F, have applications in numerous elds, including machine learning, statistical estimation, and simulation-based optimization [65,23,54]. The current accepted methodology for such problems is the stochastic (sub)gradient metho”
Learning from Conditional Distributions via Dual Embeddings (2016, background): “More general results of interchangeability between maximization and integration can be found in (Rockafellar and Wets, 1998, Chapter 14) and (Shapiro and Dentcheva, 2014, Chapter 7).”
Multi-stage distributionally robust optimization with risk aversion (2021, methodology): “A two-stage stochastic linear programming model can be formulated as follows (see [46, 8]), min x∈X cx+ E[Q(x, ξ)], (1)”
Stochastic model predictive control for economic/environmental operation management of microgrids: An experimental case study (2016, methodology): “We propose the use of MPC in combination with mixed integer linear programming (MILP) [52,53] and two-stage stochastic programming [54]; we will refer the proposed novel control scheme for microgrid management as MG-SMPC.”
Statistical estimation of composite risk functionals and risk optimization problems (2015, methodology): “However, the riskmeasure for p = 1 has an equivalent min–max formulation, for which a Central Limit Theorem has already been derived in the literature (see, Shapiro 2008; Shapiro et al. 2009, Section 6.5).”