ABSTRACT
The use of nonlinear programming in solving hydrosystems problems has not been as widespread, even though most of the problems requiring solutions are nonlinear problems. Unconstrained and constrained nonlinear optimization procedures are described, followed by a description of the augmented Lagrangian penalty function method and its application to discrete-time optimal control problems. This chapter describes the basic concepts of unconstrained nonlinear optimization, including the necessary and sufficient conditions of a local optimum. Understanding unconstrained optimization procedures is important because these techniques are the fundamental building blocks in many of the constrained nonlinear optimization algorithms. The line search techniques for solving one-dimensional optimization problems form the backbone of nonlinear programming algorithms. The most important theoretical results for nonlinear constrained optimization are the Kuhn-Tucker conditions. The essential idea of penalty function methods is to transform constrained nonlinear programming problems into a sequence of unconstrained optimization problems.
