求解伪单调变分不等式的新的自适应投影算法

New Self-Adaptive Projection Method for Solving Pesudomotone Variational Inequalities

考虑求解一类变分不等式问题的新的自适应投影算法,该算法改进了搜索的方向和步长,改进的方向、步长在解点附近均不趋于0,保证算法的快速收敛性。并在伪单调的条件下证明了算法是全局收敛的,使得该算法的适用性更广。数值实验表明算法是有效的。

We propose a new self-adaptive projection method with improved direction and stepsize for solving variational inequality problems. The improved direction and step-size will not be zero when the iteration is near the solution, which make the method converge quickly. We proved that under the condition that the function F is pesudomotone, the sequence generated by the meth- od converges to a solution of the variational inqueality problem globally, thus the method can be used extensively. Some preliminary computational results are reported, which illustrate that the new method is efficient.