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

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.