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1)  Broyden-like algorithm
类Broyden算法
1.
In this paper, we present a Broyden-like algorithm for solving bi-obstacle problems based on its equivalent B-differentiable equations.
针对双障碍问题,本文提出了与其等价的B可微方程的类Broyden算法,并 在一定条件下证明了该算法的全局收敛性和超线性收敛性。
2)  Broyden class
Broyden算法类
3)  Broyden methods
Broyden算法
1.
In this paper,a class of improved Broyden methods are presented, and the global convergence properties of the improved Broyden methods (except for DFP)are shown.
提出了一组求解无约束优化问题的改进的 Broyden算法 ,并给出了算法的全局收敛性结果 (不包括 DFP算法 )。
2.
In this paper,we present a family of modified Broyden method with wolfe-line search for solving nonconvex minimization problems,if we assume the objective function is twice continuously differentiable,the Hessian matrix G(x) of f(x) is positive definite at x * and G(x) is Lipschitz at x * ,we will prove global superlinear convergence of the modiffied Broyden methods.
提出了一种求解非凸函数极小的修正的Broyden算法 ,该算法的基本思想是对计算Broyden修正矩阵的梯度差增加一个修正项。
4)  Block Broyden algorithm
块Broyden算法
5)  Broyden method
Broyden算法
1.
A Broyden method,which has been used in the device simulation domain,is described and used to self-consistently solve the electron density and electric potential of a 1D semiconductor quantum line.
利用Broyden算法,通过自洽求解一维半导体量子线的电子浓度分布和电势分布,和常用的牛顿法以及逐次超松弛(SOR)法相比较,确认了Broyden算法的收敛结果正确,并减少了达到收敛的迭代步数,是对于薛定谔方程和泊松方程组成的非线性方程组系统自洽求解的有力工具。
6)  Broyden algorithm family
Broyden算法族
1.
In this paper,We introduce the basic properties about heredity of positive definite property of revised matrix {B k}or{H k}and the conjugation of the iterative direction generated by the Broyden algorithm family.
介绍无约束优化的Broyden算法族的基本性质 ,即算法产生的校正矩阵 {Bk}或 {Hk}的正定传递性以及产生的迭代方向的共轭性 ,这些性质是其他优化算法不具备的 ,还介绍了Huang算法族及它的重要性
补充资料:Broyden method
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性质:一种非线性方程组迭代求解方法,是一种拟牛顿法。将方程组表示为F(X)=0,则迭代公式为X(k+1)=X(k)+H(k)F[X(k)]其中△X(k)=X(k+1)-X(k),△F(k)=F[X(k+1)]-F[X(k)],k为迭代次数。这种方法需要设置一个初值点和一个初始迭代矩阵。

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