非线性约束优化的既约两块校正回代算法  

A TWO-PIECE UPDATE REDUCED HESSIAN ALGORITHM WITH BACKTRACKING TECHNIQUE FOR CONSTRAINED OPTIMIZATION

作　　者：顾益明[1] 朱德通[1] 

机构地区：[1]上海师范大学数学系,上海200234

出　　处：《高等学校计算数学学报》2005年第S1期329-335,共7页Numerical Mathematics A Journal of Chinese Universities

基　　金：上海师范大学校科研基金(DKL311)资助.

摘　　要：1 引言本文考虑非线性等式约束优化问题其中f:Rn→R是连续可微函数,c(x):Rn→Rm(m≤n)为非线性实值函数．记g(x)表示目标函数f(x)的梯度▽f(x)∈Rn,用A(x)表示约束函数的雅可比矩阵,即A(x)=▽c(x):[▽c1(x),…,▽cm(x)]∈Rn×m．定义拉格朗日函数l(x,λ)We propose a two-piece update of projected Hessian algorithm with backtracking technique for solving nonlinear equality constrained optimization problems. To deal with large problems, a two-piece update of two-side-reduced Hessian is used to replace the full Hessian matrix. By adopting the Fletcher s penalty function as the merit function, a nonmonotonic backtracking trust region strategy is suggested which does not require the merit function to its value in every iteration. The proposed algorithm which swi...

关 键 词：trust region BACKTRACKING reduced. 

分 类 号：O241.82[理学—计算数学]