关键词: 修正Lagrangian算法, 非线性约束优化问题, 局部收敛, 误差界

Abstract: 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 solvingsome simple constrained optimization problems are illustrated.

Key words: Modified Lagrangian algorithm, Nonlinearconstrained optimization problems, Local convergence, Error bound