锥模型拟牛顿法  

CONIC MODEL QUASI-NEWTON METHOD

作　　者：杨富贵[1] 盛松柏[2] 

机构地区：[1]唐山工程技术学院,063009 [2]南京航空航天大学理学院,210016

出　　处：《高等学校计算数学学报》1995年第4期323-331,共9页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金;江苏省自然科学基金

摘　　要：1 引 言 对于求解无约束最优化问题 min f(x),f:R^n→R,f∈C^2。Davidon提出了一类非二次模型方法,即锥函数近似模型 f(x)≈c(x)=f(x_k)+(f(x_k)~T(x-x_k))/((1-h_k^T(x-x_k))+1/2((x-x_k)~TA_k(x-x_k))/([1-h_k^T(x-x_k)]~2) (1.1)Davidon (1980) proposed a class of collinear scaling algorithms with conic function for unconstrained minimization. Some authors have presented that a certain family of algorithms contained in this class may be considered as an extension of the family of quasi-Newton methods with Broyden family of approximants of the objective function Hessian. In this paper, without the collinear scaling transformation, we directly derive a class of conic model algorithms by using the interpolating conditions (i. e. , the function values and gradients at the iterative points xk-1 and xk.) The new methods may be considered as an extension of the quasi-Newton method with quadratic model, but they are different from Sorensen's or Ariyawansa' s methods.

关 键 词：锥模型 拟牛顿法 无约束最优化 最佳化 

分 类 号：O242.23[理学—计算数学]