ABSTRACT
This chapter deals with zeroth order and some first-order methods. Generally, the field of optimization was initially an outgrowth of mathematical departments and mathematicians who came up with neat and useful methods. Performance requirements on a device to be synthesized through optimization are cast as minimizing an object function defined in terms of the parametric description of the device being designed. Engineering optimization is a field that was pioneered by structural engineers, a field led by such intellectual giants as O. C. Zienkiewicz and G. H. Gallagher and Garret N. Vanderplaats. The simplest way to understand optimization is to start with a function of a single variable. Powell’s method is one such method employing the univariate search to reduce searching for the minimum in a multi-dimensional space to a sequence of one-dimensional univariate searches. The genetic algorithm is a zeroth-order method of optimization suited to multi-dimensional problems, especially ones with multiple local minima.
