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.
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.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2006年第1期49-62,共14页
Acta Mathematica Scientia
基金
国家青年自然科学基金(10001007)
武汉理工大学博士科研基金资助