2.1 Introduction

Optimization is important for engineers for a number of reasons:

• A best design finds the maximum of some benefit function.
• Drag reduction minimizes drag.
• Potential energy minimization finds the stationary state of a system. That is the basis for true finite element methods.
• Much of economics is based on finding the extrema of cost or benefi functions.
• ...

Key ideas:

• zero partial derivatives at an interior extremum
• Lagrangian multipliers can account for constraints