Numerical Methods for Convex Multistage Stochastic Optimization by Guanghui Lan

Description: Numerical Methods for Convex Multistage Stochastic Optimization by Guanghui Lan, Alexander Shapiro Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). This monograph concentrates on SP and SOC modeling approaches. In these frameworks, there are natural situations when the considered problems are convex. FORMAT Paperback CONDITION Brand New Publisher Description Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). This monograph concentrates on SP and SOC modeling approaches. In these frameworks, there are natural situations when the considered problems are convex. The classical approach to sequential optimization is based on dynamic programming. It has the problem of the so-called "curse of dimensionality", in that its computational complexity increases exponentially with respect to the dimension of state variables.Recent progress in solving convex multistage stochastic problems is based on cutting plane approximations of the cost-to-go (value) functions of dynamic programming equations. Cutting plane type algorithms in dynamical settings is one of the main topics of this monograph. Also discussed in this work are stochastic approximation type methods applied to multistage stochastic optimization problems. From the computational complexity point of view, these two types of methods seem to be complimentary to each other. Cutting plane type methods can handle multistage problems with a large number of stages but a relatively smaller number of state (decision) variables. On the other hand, stochastic approximation type methods can only deal with a small number of stages but a large number of decision variables. Table of Contents 1. Introduction2. Stochastic Programming3. Stochastic Optimal Control4. Risk Averse and Distributionally Robust Optimization5. Dynamic Cutting Plane Algorithms6. Computation Complexity of Cutting Plane Methods7. Dynamic Stochastic Approximation Algorithms8. ConclusionsAcknowldgementsReferences Details ISBN1638283508 Author Alexander Shapiro Pages 94 Publisher now publishers Inc Series Foundations and Trends® in Optimization Year 2024 ISBN-13 9781638283508 Format Paperback Publication Date 2024-05-22 Imprint now publishers Inc Place of Publication Hanover Country of Publication United States Alternative 9781638283515 Audience Professional & Vocational US Release Date 2024-05-22 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:160323228;

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