【摘要】 本文中我们对Nocedal与Overton所提出的双边投影拟牛顿方法加以改进,增添一个修正项。这个修正项的计算量是很少的,但修改后的方法可以同时改进局部收敛性与全局性收敛性。本文将集中讨论局部收敛性,特别是证明了在使用DFP或PSB等矩阵校正公式时,修正后的方法在一定的条件下是超线性收敛的。对于全局收敛性的讨论将另文给出。更多还原

【Abstract】 We revise Nocedal-Overton’s two-sided projected quasi-Newton method for equality constrained optimization problems by adding a correction term which requires only a little additional computation effort, nevertheless improves, both local convergence and global convergence. This paper is focused on the discussion of the local property. Particularly, it is proved that if DFP or PSB matrix updating formulae are used, then our method will be convergent superlinearly under some conditions. Global convergence of the method will be dealt with in a forthcoming paper.更多还原