Computational Stochastic Programming Models, Algorithms, and Implementation--计算随机规划模型、算法及其实现

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Springer Optimization and Its Applications 774

LewisNtaimo

Computational

Stochastic

Programming

Models, Algorithms, and

Implementation

Springer Optimization and Its Applications

Volume 774

Series Editors

Panos M. Pardalos , University of Florida, Gainesville, FL, USA

My T. Thai , CSE Building, University of Florida, Gainesville, FL, USA

Honorary Editor

Ding-Zhu Du, University of Texas at Dallas, Richardson, TX, USA

Advisory Editors

Roman V. Belavkin, Faculty of Science and Technology, Middlesex University,

London, UK

John R. Birge, University of Chicago, Chicago, IL, USA

Sergiy Butenko, Texas A&M University, College Station, TX, USA

Vipin Kumar, Dept Comp Sci & Engg, University of Minnesota, Minneapolis, MN,

USA

Anna Nagurney, Isenberg School of Management, University of Massachusetts

Amherst, Amherst, MA, USA

Jun Pei, School of Management, Hefei University of Technology, Hefei, Anhui,

China

Oleg Prokopyev, Department of Industrial Engineering, University of Pittsburgh,

Pittsburgh, PA, USA

Steffen Rebennack, Karlsruhe Institute of Technology, Karlsruhe, Baden-

Württemberg, Germany

Mauricio Resende, Amazon (United States), Seattle, WA, USA

Tamás Terlaky, Lehigh University, Bethlehem, PA, USA

Van Vu, Department of Mathematics, Yale University, New Haven, CT, USA

Michael N. Vrahatis, Mathematics Department, University of Patras, Patras, Greece

Guoliang Xue, Ira A. Fulton School of Engineering, Arizona State University,

Tempe, AZ, USA

Yinyu Ye, Stanford University, Stanford, CA, USA

Aims and Scope

Optimization has continued to expand in all directions at an astonishing rate. New

algorithmic and theoretical techniques are continually developing and the diffusion

into other disciplines is proceeding at a rapid pace, with a spot light on machine

learning, artiﬁcial intelligence, and quantum computing. Our knowledge of all

aspects of the ﬁeld has grown even more profound. At the same time, one of the

most striking trends in optimization is the constantly increasing emphasis on the

interdisciplinary nature of the ﬁeld. Optimization has been a basic tool in areas

not limited to applied mathematics, engineering, medicine, economics, computer

science, operations research, and other sciences.

The series Springer Optimization and Its Applications (SOIA) aims to publish

state-of-the-art expository works (monographs, contributed volumes, textbooks,

handbooks) that focus on theory, methods, and applications of optimization. Topics

covered include, but are not limited to, nonlinear optimization, combinatorial opti-

mization, continuous optimization, stochastic optimization, Bayesian optimization,

optimal control, discrete optimization, multi-objective optimization, and more. New

to the series portfolio include Works at the intersection of optimization and machine

learning, artiﬁcial intelligence, and quantum computing.

Volumes from this series are indexed by Web of Science, zbMATH, Mathematical

Reviews, and SCOPUS.

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摘要：

本文档深入探讨了计算随机规划的核心理论、模型构建、高效算法及其实际实现方法，系统覆盖了从基础概率建模到复杂场景下的决策优化全过程。内容首先阐述了两阶段与多阶段随机规划的标准数学框架，详细讲解了如何以有限场景或分布鲁棒方式处理不确定性；其次重点剖析了Benders分解、渐进对冲算法、随机对偶动态规划等主流求解技术的原理与适用条件，并结合收敛性分析与复杂度评估指导算法选择；最后通过具体的编程实现案例（包括Python/Julia/Matlab的常用优化库调用）展示了数值实验设计、场景生成与缩减、以及

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