Design Theory and Methods using CAD/CAE

3.3. Optimality Conditions

A basic knowledge of optimality conditions is important for understanding the performance of the various numerical methods discussed later in the chapter. In this section, we introduce the basic concept of optimality, the necessary and sufficient conditions for the relative maxima and minima of a function, as well as the solution methods based on the optimality conditions. Simple examples are used to explain the underlying concepts. The examples will also show the practical limitations of the methods.

3.3.1. Basic Concept of Optimality

We start by recalling a few basic concepts we learned in Calculus regarding maxima and minima, followed by defining local and global optima; thereafter, we illustrate the concepts using ...