Adaptive Stochastic Optimization Techniques with Applications

3  Dynamic Optimization Techniques and Optimal Control

3.1  Introduction

Dynamic optimization techniques reflect a development of the classical optimization programming techniques, which allows for the handling of time variant problems. Optimization over time in a single- or multi-stage decision process is generally formulated as dynamic programming (DP), involving large number of variables under different stages [1,2,3,5,7].

Here, an overview of optimal control, dynamic programming, and underlying concepts such as the generalized Hamiltonian-Jacobi, Pontryagin’s principle, and Bellman’s optimality conditions is presented [3,4]. Expansion of the DP to handle nondeterministic or random processes has led to the development of stochastic DP ...