基于非线性约束优化问题,讨论了外罚函数法与广义Lagrange乘子法,并通过MATLAB编程实现了两种算法.实验表明:(1)广义Lagrange乘子法在迭代次数和收敛结果上优于外罚函数法且对初始点的选取要求不高;(2)广义Lagrange乘子法的罚因子的修正系数不宜过大,一般在区间(1,2)上取值,广义Lagrange乘子法更具优越性.最后,通过3个工业工程中的非线性规划实际问题说明乘子法比外罚函数法具有更广泛的实用性.%Based on the nonlinear constrained optimization problem,this paper discussed the external penalty function method and the generalized lagrangian multiplier method,and two algorithms have been implemented by programming.The experimental results show that:(1) The generalized multiplier method is superior to the external penalty function method in the iteration times and the convergence results,and the selection of the initial point is not strict.(2) The correction factor of the penalty factor of the generalized multiplier method should not be too large,evaluating on the interval (1,2) is more superior.Finally,the practical problems of nonlinear programming in three industrial projects show that the generalized lagrangian multiplier method has more practicability than the external penalty function method.
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