凸约束伪单调方程组的无导数投影算法

A DERIVATIVE-FREE PROJECTION ALGORITHM FOR SOLVING PSEUDO-MONOTONE EQUATIONS WITH CONVEX CONSTRAINTS

基于HS共轭梯度法的结构,本文在弱假设条件下建立了一种求解凸约束伪单调方程组问题的迭代投影算法.该算法不需要利用方程组的任何梯度或Jacobian矩阵信息,因此它适合求解大规模问题.算法在每一次迭代中都能产生充分下降方向,且不依赖于任何线搜索条件.特别是,我们在不需要假设方程组满足Lipschitz条件下建立了算法的全局收敛性和R-线收敛速度.数值结果表明,该算法对于给定的大规模方程组问题是稳定和有效的.

Based on the structure of the HS conjugate gradient method,we propose an iterative projection algorithm for solving nonlinear pseudo-monotone equations with convex constraints under one weak assumption.Since the proposed method does not need any gradient or Jacobian matrix information of equations,it is suitable to solve large-scale problems.The proposed algorithm generates a sufficient descent direction in per-iteration,which is independent of any line search.Moreover,the global convergence and R-linear convergence rate of the proposed method are proved without the assuniption that nonlinear equations satisfies Lipschitz condition.The numerical results show that the proposed method is stable and effective for the given large-scale nonlinear equations with convex constraints.