摘要
采用Lanczos法构成路径解线性等式约束的非线性优化问题．通过构造预处理Lanc- zos路径解目标函数的二次近似模型获得下降搜索方向．基于预处理Lanczos路径的性质,在合理的假设条件下,证明了所提供的算法不仅具有整体收敛性,而且保持快速的超线性收敛速率．进一步,数值计算表明了算法的可行性和有效性．
We propose a preconditioned Lanczos path algorithm for constrained linear equality optimization. Employing the preconditioned Lanczos path search strategy, we obtain an iterative direction by solving a quadratic model, which makes the objective function monotonically decreasing. Theoretical analysis is given which proves that the algorithm is globally convergent and has a local super linear convergence rate under some reasonable conditions. Finally ,numerical results are provided which indicate that the algorithm is effective.
出处
《上海师范大学学报（自然科学版）》
2007年第1期7-11,共5页
Journal of Shanghai Normal University(Natural Sciences)
基金
上海市教委基金(05DZ11)资助
上海重点学科(T0401).
