Abstract: 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 the programming theory the dual conditions of constraint are linear algebraic polynomials, and the dual object function is a nonlinear monomial. The paper presents an approach of reduction and iteration for GP which transforms primary functions of original GP into approximate monomials based on Duffin formula, and dual object function into an approximate linear polynomial. Thus solved dual programming is a linear programming problem and an approximate optimum solution can be obtained simply. By means of iteration approach the real optimum of original GP can be solved. The paper offers the steps of solving process on computer. At the end two examples of sketchy design for airplane (the optimum distribution of aileron supports, the optimum layout of parameters for aircraft global configuration) are explained for solving process and the solutions, compared with the given results. It can be shown that the approach presented in the paper is correct, simple and useful for engineering design, even to Expert System or Artificial Intelligence.

Key words: optimiza tion design, mathematical progr amming, geomet ric pr ogramming, air plane design