有界变量约束非线性不定方程组的仿射信赖域内点算法(英文)  

An affine scaling trust-region algorithm with interior backtracking technique for solving bound-constrained underdetermined nonlinear systems

作　　者：袁液[1] 贾春霞[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2010年第2期137-143,共7页Journal of Shanghai Normal University(Natural Sciences)

基　　金：Support by the National Science Foundution Grant of China(10471094)

摘　　要：通过引入指示函数及其相应的指示集合和强二阶充分条件,在不需要严格互补条件的情况下,所提供的算法不仅有整体收敛于方程组的解且保持局部超线性收敛速率.最后,数值试验表明算法的可行性与有效性.An affine scaling trust-region algorithm with interior backtracking technique,which is introduced in [ 9 ] for solving square nonlinear systems with simple bounds, is modified and extended to cope with the underdetermined case with simple bounds. By introducing the identification functions, we prove the global and local convergence when thestrict complementarity is not required. In addition, we discuss the superlinear convergence rate of the proposed algorithm. Finally, numerical experiments are presented to explain the feasibility and effectiveness of the proposed algorithm.

关 键 词：非单调技术 不定线性方程 内点 信赖域 指示函数 

分 类 号：O221.2[理学—运筹学与控制论]