ABSTRACT
Deterministic optimization, or mathematical programming, is the classical way to perform optimization through mathematical models. This chapter discusses the solution of nonlinear programming problems to illustrate the main characteristics of the mathematical programming methods for the solution of optimization problems. It deals with the simplest type of mathematic optimization, which is an unconstrained, one-variable optimization problem. For multivariable optimization, two important concepts are continuity and convexity. The chapter describes continuity and convexity of functions, and discusses the importance of such properties on optimization. Because most of the deterministic optimization methods are based on the calculation of derivatives, dealing with continuous functions ensures that the derivatives exist for all feasible regions. To solve an unconstrained optimization problem, a gradient-based approach can be used. The chapter examines a couple of methods for equality-constrained optimization. A more general optimization problem involves a feasible region bounded by equality and inequality constraints.
