Numerical Methods and Optimization

Chapter 8

Basic Concepts

Optimization is a methodology aiming to find the best among available al-

ternatives. The available alternatives are referred to as feasible solutions,and

their quality is measured using some numerical function called the objective

function. A feasible solution that yields the best (minimum or maximum)

objective function value is called an optimal solution.

Optimization problems are of great practical interest. For example, in man-

ufacturing, how should one cut plates of a material so that the waste is min-

imized? In business, how should a company allocate the available resources

so that its profit is maximized? Some of the