求正项式几何规划全局解的线性化方法

Linearization Method for Solring Global Solution of Posynomial Geometric Programming

对正项式几何规划问题(PGP)提出一近线性化方法,这类优化问题能广泛应用于工程设计非线性系统的鲁棒稳定性分析等实际问题中。使用指数变换及利用分段线性化技术转变每个指数项为一些带绝对值项的和,再将绝对值项线性化,最终将原问题转化为一个线性规划问题。数值实验表明,本文的方法是可行的,能近似地求其问题(PGP)的全局最优解。

In this paper a linearization method global optimization algorithm is proposed for locating the global minimum of the posynomial geometric programming （PGP）, which can be applied to engineering designs and robust stability analysis of nonlinear systems and other pratical problems. By utilizing an exponential transformation and piecewise linearization tech- nique, transforming the exponential terms into the sum of absolute terms, and linearizing each absolute term, the original problem can be transformed into a linear programming problem which can be easily solved. And finally the numerical exper- iments results are given to illustrate the feasibility of the proposed algorithm,which can approaximately obtain the global solution of the （PGP）.