NUMERICAL OPTIMIZATION CONCEPTS AND DEFINITIONS

The basic concepts of Numerical Optimization are described geometrically and defined mathematically. This leads to a compact statement of the general nonlinear optimization problem and the typical iterative approach to its solution. The optimization process is further described with a simple numerical example which demonstrates the conversion of the original design task to the numerical optimization task. Here the concept of the design space is introduced and the necessary mathematical conditions for optimality are given. Typical methods for solution of the numerical optimization problem are identified. The importance of proper problem formulation is emphasized as a means of ensuring efficiency and reliability. A general program structure for design is offered which makes the progression from analysis to optimization straightforward. The state of the art is such that problems in the category of twenty design variables and hundreds of constraints can be routinely solved. Most importantly, using available software, a design program can now be created with little effort beyond that necessary for analysis. It is concluded that numerical optimization is an efficient, versatile design tool for solution of a wide variety of design tasks, from the routine to the exotic.