一个等式约束问题的拟Newton-信赖域型方法及其收敛性

A Quasi-Newton-Trust Region Methodfor Equality Constrained Optimizationand Its Convergence Properties

在[1]中,Vardi提出一个信赖域方法,而收敛性证明却是在精确λ-搜索下给出的.本文在[1]的基础上提出一个新的算法-拟Newton-信赖域型算法,并证明该算法是全局收敛的.通过利用二阶修正技术去修正该算法,我们证明了该算法是局部超线性收敛的.

In [1], Vardi proposed a trust region algorithm for equality constrained optimization, but the global convergence was obtained under exact A-search. In this paper, we propose a new method-quasi-Newton-trust region algorithm, which is based on the method in [1] and prove that it is convergent. By using twice order correction technique to modify the algorithm, we prove that the algorithm is convergent superlinearly.