非线性约束优化问题的一个修正Lagrangian算法  

A Modified Lagrangian Algorithm for Solving Nonlinear Constrained Optimization Problems

作　　者：贺素香[1] 张立卫[2] 

机构地区：[1]武汉理工大学理学院,武汉430070 [2]大连理工大学应用数学系,大连116024

出　　处：《数学物理学报（A辑）》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

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.

关 键 词：修正Lagrangian算法 非线性约束优化问题 局部收敛 误差界 

分 类 号：O221[理学—运筹学与控制论]