求解变分不等式的非单调混合Newton算法

A Non-monotone Hybrid Newton Method for Solving the Variational Inequality Problems

本文运用广义D-间隙函数可以将变分不等式问题转化为一个无约束最优化问题,即极小化广义D-间隙函数的一般形式gαβ,基于非单调线搜索技术提出一种非单调混合Newton算法,并给出了算法的全局收敛性分析.在适当条件下,证明了算法具有全局二次收敛性.同时在映射F强单调但不需要Lipschitz连续的情况下,为算法提供了一个全局误差界.数值结果表明新算法是有效的.

In this paper, the variational inequality problem is transformed as an unconstrained optimization problem through the generalized D-gap function. A non-monotone hybrid Newton method based on Zhang H.C.＇s non-monotone line search technique is proposed for minimizing the general form of the generalized D-gap function. Then, the global convergence property of the algorithm is analyzed. Under some proper conditions, we prove that the algorithm is globally quadratically convergent. Moreover, we obtain a global error bound of the algorithm when the mapping F is strongly monotone without Lipschitz continuous. Numerical results indicate that the new algorithm is efficient.