基于中间变量的乘子法

Multiplier method based on intermediate variables

为了更有效地用乘子法求解结构优化问题,将倒变量和混合变量这两种中间变量引入乘子法,提出了基于中间变量的乘子法。在这种新方法中,基于增广拉格朗日函数的无约束子问题的构造和求解,以及算法的迭代和收敛,都是对中间变量进行的。只有目标函数与约束函数的函数值及梯度值的求取,是对原变量进行的。用两个具有较高非线性的工程算例对新方法进行测试,测试结果表明新方法具有良好的收敛性,且比一般的乘子法的收敛速度更快。

In order to use multiplier method to solve structural optimization problem more effectively, two kinds of intermediate variables, reciprocal variable and mixed variable, are introduced into multiplier method, and a new multiplier method based on intermediate variables is proposed. In the new method, the construction and solution of the unconstrained subproblem based on augmented Lagrange function, and the iteration and convergence of the arithmetic are all in line with intermediate variables. Only the value and gradient of objective function and constraint functions are achieved in line with original variables. Two simulation examples with high nonlinearity are adopted to test the new method, and the results show that the new method has good conver- gence and has faster convergence speed than common multiplier method.