This paper discussed the theorem of the average arithmetic geometric mean of algebraic polynomials systematically, then derived and analyzed the original geometric programming (GP) briefly.

In fact, there are some very old books that show this as the average, the sum divided by two arithmetic mean, but the modern practice is to use the geometric mean.

Then, formulate a general weight function based on weight arithmetic, weight geometric and weighted harmonic mean, which provides math mean for the study.