用实数同伦法确定机械优化问题的多个解

提出用实数同伦法[1]确定机械优化问题的多个解的方法。其核心思想是:根据K-T条件将一个非线性规划问题转化成一个非线性方程组的求解问题,并用实数同伦法在实数域上数值求解该非线性方程组,进而获得原优化问题的所有或绝大多数局部最优解。文中建立了统一的求解模型,并解决了数值计算中的若干问题,从而使本文提出的方法达到了较为实用的程度

To Determine Multiple Solutuons of Mechanical Optimization Problem by Real Number Homotopy Method

In this paper,the method is suggested to determine multiple solutions of mechanical optimization problem by real number homotopy method.The main idea is first to transform a problem of nonlinear programming into a problem of nonlinear system of equations,then solve the nonlinear system of equations by real number homotopy method in the real field,and finally find all or an overwhelming majority of local optimum solutins.The uniform model for solving optimization problem has been built up,and some problems about numerical calculation have been solved,so the method put forward in this paper is rather practical.All that is done in this paper is rather valuble either in theory or in application.