求解等式约束最优化问题的Broyden算法的全局收敛性

Global Convergence of Broyden's Method for Equality Constrained Optimization Problems

将单边既约Hesse矩阵SQP方法和无导数线性搜索技术相结合,提出了一种求解等式约束最优化问题的拟牛顿算法.在适当的假设条件下,证明了算法全局收敛于优化问题的KKT点,而且收敛速度是局部超线性的.当迭代次数k充分大时,这种算法可以实现单位步长,因此不会出现Marotos效应.

By combiming a derivativefree line search with the projected heasian SQP methods,a quasiNewton method for solving equality constrained optimization problems was proposed.Under appropriate conditions,it is showed that the proposed method converges to a KKT point of the problem globally and superlinearly.Moreover,when the iterative number k sufficiently large,the unit step length would be favorite.As result,the Marotos effect may be avoided.