凸约束优化的非单调信赖域算法的收敛性  

The Convergence of a Class of Nonmonotone Trust Region Algorithms for Convex Constrained Optimization

作　　者：葛恒武[1] 陈中文[1] 

机构地区：[1]苏州大学数学系,江苏苏州215006

出　　处：《应用数学》2001年第3期77-81,共5页Mathematica Applicata

摘　　要：本文对凸约束优化问题提出一类新的非单调信赖域算法 ,在二次模型 Hesse矩阵{ Bk}一致有界条件下 ,证明了算法具有强收敛性 ;在 { Bk}线性增长的条件下 ,证明了算法具有弱收敛性 ;这推广了现有线性约束或凸约束优化问题的各种信赖域算法 。The authors present a new class of and more general nonmono to ne trust region algorithms for convex constrained optimization. Under the assump tion which the Hessian matrices {B k} of the quadrtic model are uniformly b ounded, the strong global convergence is proved. We also prove the weak global c onvergence of the algorithm if the matrix sequence {B k} increases linearly , which generalize the scope that the various trust region algorithms can be app lied and improved the global convergence results theorectially.

关 键 词：凸约束 信赖域算法 非单调算法 全局收敛性 优化问题 二次模型 HESSE矩阵 强收敛性 

分 类 号：O224[理学—运筹学与控制论]