Numerical Methods for Convex Multistage Stochastic Optimization by Guanghui Lan

Numerical Methods for Convex Multistage Stochastic Optimization by Guanghui Lan

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.

SKU	Unavailable
ISBN 13	9781638283508
ISBN 10	1638283508
Title	Numerical Methods for Convex Multistage Stochastic Optimization
Author	Guanghui Lan
Series	Foundations And Trends® In Optimization
Condition	Unavailable
Binding Type	Paperback
Publisher	now publishers Inc
Year published	2024-05-22
Number of pages	94
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable