Transformer design optimization falls into the most general category of such methods, namely, nonlinear equality- and inequality-constrained optimization. Optimization is a fairly large branch of mathematics with major specialized subdivisions such as linear programming, unconstrained optimization, and linear or nonlinear equality- or inequality-constrained optimization. This chapter describes geometric programming, presenting enough of the formalism to appreciate some of its strengths and weaknesses. Geometric programming requires that the function be minimized, the objective or cost function and all the constraints be expressed as posynomials. When the degree of difficulty is not zero, the method becomes one of maximizing a nonlinear function subject to linear constraints for which various solution strategies are available. In the case of transformer design optimization, the number of terms in a realistic cost function, not to mention the constraints, is quite large, whereas the number of design variables can be kept reasonably small.