基于单调性分析和GROEBNER基法的符号优化方法

An approach for symbolic optimization based on monotonicity analysis and method of groebner bases

本文提出了一种用Ｇｒｏｅｂｎｅｒ基法求基于单调性分析的优化设计问题符号形式最优解的方法。该法对优化问题的从单调性分析得出的子问题的等价方程组直接求解，根据该方程组的特点建立了方程项和变量的排序的法则，从而快速地得到以三角化Ｇｒｏｅｂｎｅｒ基形式表示的优化问题的符号形式的最优解。文中具体算例说明了方法的有效性和优点。

By the use of Groebner bases method and based on the monotonicity analysis this paper put forward a kind of approach for determining the symbolic formed optimum solution on the issue of optimization design.A direct solution is made by this method on the equivalent equation set of subproblems obtained from the monotonicity analysis on the optimization problems.In accordance with the characteristics of this equation set the ordering rules for terms and variables of equations are established,thus the symbolic formed optimum solution of the optimization problems,expressed in the form of triangularized Groebner bases,can be obtained rapidly.A concrete example of calculation illustrated the effectiveness and merit of this method.