凸约束非线性方程组的一种无导数投影方法

A Derivative-Free Projection Method for Solving Nonlinear Equations with Convex Constraints

推广LCG共轭梯度方法并建立一种求解凸约束非线性单调方程组问题的无导数投影方法．在适当的条件下，证明了方法的全局收敛性．方法不需要任何导数信息，而且继承了共轭梯度方法储存量小的特征，因此它特别适合求解大规模非光滑的非线性单调方程组问题．大量数值结果和比较表明方法是有效的和稳定的．

In this paper, a derivative-free projection method is proposed for solving nonlin- ear monotone equations with convex constraints, which is a generalization of LCG conjugate gradient method. Under some suitable conditions, we prove the global convergence of the pro- posed method. The proposed method does not need any derivative information, and inherits the characteristics of the conjugate gradient method, so it is especially suitable for solving the large-scale non-smooth nonlinear monotone equations. A large number of numerical results and comparisons show that the proposed method is effective and stable.