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系统地讨论了代数多项式的算术－ 几何均值定理，并对原型几何规划理论作出了简明的推导与分析。提出了具有缩并迭代特性的几何规划求解理论和编程步骤。还用２ 个工程设计的优化求解算例来说明这种缩并迭代几何规划优化求解特点和优点。例１ 显示了几何规划的工程实用性和简易性；例２ 通过轻型飞机总体方案参数优化，说明所提出的优化方法，可随设计人员思路的变动而得到及时地相适应。
The arithmetic-geometric mean theorem of algebraic polynomials is systematically discussed, and a brief derivation and analysis of prototype geometry programming theory is made. Proposed geometric programming solution theory and programming steps with the characteristics of degenerate iteration. Two engineering optimization solution examples are also used to demonstrate the features and advantages of this de-iteration geometry optimization solution. Example 1 shows the engineering practicability and simplicity of geometric planning. Example 2 shows that the proposed optimization method can be timely adapted to changes of designers’ ideas through the optimization of light aircraft overall program parameters.