CONVERGENCE OF INEXACT CONIC NEWTON METHODS  

作　　者：胡蓉 盛松柏 

出　　处：《Numerical Mathematics A Journal of Chinese Universities(English Series)》1998年第2期159-168,共10页

摘　　要：A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton equation at each iterate. In this paper we consider an inexact conic Newton method, which solves the couic Newton equation oldy approximately and in sonm unspecified manner. Furthermore, we show that such method is locally convergent and characterizes the order of convergence in terms of the rate of convergence of the relative residuals.A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton e-quation at each iterate. In this paper we consider an inexact conic Newton method, which solves the conk Newton equation only approximately and in some unspecified manner. Furthermore, we show thai such method is locally convergent and characterizes the order of convergence in terms of the rate of convergence of the relative residuals{η_k}.

关 键 词：INEXACT CONIC NEWTON method CONIC NEWTON EQUATION relative RESIDUAL NEWTON EQUATION FORCING sequence 

分 类 号：O242.23[理学—计算数学]