等式约束非凸优化问题的修正牛顿算法（英文）  

A REGULARIZED NEWTON METHOD FOR EQUALITY CONSTRAINED NONCONVEX OPTIMIZATION

作　　者：张新华[1] 

机构地区：[1]南京农业大学工学院,江苏南京210031

出　　处：《数学杂志》2015年第1期1-11,共11页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(71001053)

摘　　要：本文设计了一个新的求解等式约束非凸优化问题的修正牛顿算法.利用修正的拉格朗日函数,通过求解线性方程组获得搜索方向,利用价值函数的线性近似模型确定步长.在没有非奇异性假设的条件下,证明了算法的全局收敛性.数值结果表明,算法是有效的.A regularized Newton method is presented in this paper to solve equality con- strained nonconvex minimization problems. Such a method is characterized by its use of the per- turbation of the Lagrangian function＇s Hessian to deal with the negative curvature. The method is based on successively solving linear systems for which effective software is readily available. The linear model of a merit function is employed to attain a sufficient reduction in a local approximation of the merit function during each iteration. Without the nonsingularity assumption of solution, the global convergence of the regularized Newton method is established. Some preliminary numerical results are reported, which show the efficiency of the method.

关 键 词：约束优化 非凸优化问题 修正牛顿法 全局收敛 

分 类 号：O221.2[理学—运筹学与控制论]