信赖域型拟Newton法的全局收敛性

GLOBAL CONVERGENCE OF QUASI NEWTON METHODS WITH TRUST REGION STRATEGIES

对一般无约束最优化问题从理论上证明了由信赖域型的Ｐｏｗｅｌ－对称－Ｂｒｏｙｄｅｎ拟Ｎｅｗｔｏｎ法与对称秩１拟Ｎｅｗｔｏｎ法产生的点列至少有一极限点是函数的稳定点．对于非线性最小二乘问题，Ｂｒｏｙｄｅｎ－Ｄｅｎｎｉｓ方法。

The gobal convergence of Powll symmetric Broyden (PSB) method and symmetric rank one (SR1) method for unconstrained minimization problems has been an open problem for many years. The present paper has two purposes. Frist, It is shown that, under mild conditions, at least one limit point of the sequence generated by PSB method or SR1 method strating with an arbitrary initial point is a strationary point of the objective if trust region rather than line search strategies is used. Second, a global convergence analysis is given for Broyden Dennis method, Betts method and Bartholomew Biggs method for nonlinear least squares problems.