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The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.

Stochastic Multi-Stage Optimization: At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming

I Preliminaries.- 1.Issues and Problems in Decision Making under Uncertainty.- 2.Open-Loop Control: The Stochastic Gradient Method.- II Decision under Uncertainty and the Role of Information.- 3.Tools for Information Handling.- 4.Information and Stochastic Optimization Problems.- Optimality Conditions for SOC Problems.- III Discretization and Numerical Methods.- 6.Discretization Methodology for Problems with SIS.- 7.Numerical Algorithms.- IV Convergence Analysis.- 8.Convergence Issues in Stochastic Optimization.- V Advanced Topics.- 9.Multi-Agent Decision Problems.- Dual Effect for Multi-Agent Stochastic I-O Systems.- VI Appendices.- A. Basics in Analysis and Optimization.- B. Basics in Probability.- References.- Index.