中文摘要：

基于一个含有控制参数的修正Lagrangian函数，该文建立了一个求解非线性约束优化问题的修正Lagrangian算法．在一些适当的条件下，证明了控制参数存在一个阀值，当控制参数小于这一阀值时，由这一算法产生的序列解局部收敛于问题的Kuhn-Tucker点，并且建立了解的误差上界．最后给出一些约束优化问题的数值结果．

英文摘要：

A modified Lagrangian algorithm for solving nonlinear constrained optimization problems is established, which is based on a modified Lagrange function with a controlling parameter. Under suitable conditions, the local convergence of the modified Lagrangian algorithm is proved and the error bounds of solutions are established, which shows that there exists a threshold of the parameter such that, when the parameter is less than this threshold, the sequence of points generated by the algorithm converges to a Kuhn-Tucker point locally. Numerical results by using the modified Lagrangian algorithm for solving some simple constrained optimization problems are illustrated.