关于拟牛顿法求解等式约束优化问题的超线性收敛条件

On the Local Superlinear Convergence of QuasiNewton Method for Constrained Optimization Problems

拟牛顿法是求解约束优化问题的有效方法之一，许多作者在理论上讨论了此类算法的全局收敛性和收敛速度，但关于收敛速度的条件讨论较少．Ｂｏｇｇｓ等人给出了一个拟牛顿方法求解等式约束优化问题的超线性收敛的充要条件，但假设条件较强．本文利用分析和代数的技巧，在较弱的条件下证明了该算法的超线性收敛的充要条件仍然成立．

QuasiNewton method is an effective one for solving the equality constrained optimization problems. The global convergence and local superlinear convergence of the method have been discussed by many authors, however the condition on the superlinear convergence is fewer discussed. Boggs et al gave a necessary and sufficient condition for the local superlinear convergence of quasiNewton method for solving the problems. But the condition is stronger. By use of the technique of analysis and algebra, a result under the weaker conditions is given here.