求解单调变分不等式的下降型部分并行分裂LQP交替方向法

A Descent Partial Parallel Splitting LQP Alternating Direction Methods for Solving Monotone Variational Inequalities

对于带有三个可分离算子的结构型单调变分不等式问题,结合部分并行分裂算法和LQP交替方向法构造了一个下降方向,并沿着这个下降方向利用效益函数的一个下界给出了最优步长,提出了一种下降型部分并行分裂LQP交替方向法.在较弱的假设条件下证明了新算法的全局收敛性,并将该算法与其他算法的下降量下界进行比较,证明了新算法的优越性.

For monotone separable structure variational inequality problem with three constraint variables,combining the Partial parallel splitting method and the LQP alternating direction method,a descent direction is obtained and an appropriate step size is derived that along this descent direction and according to benefit function of a lower bound,a descent partial parallel splitting LQP alternating direction methods is obtained.and then we prove the global convergence of the algorithm under a weaker assumption.The new algorithm was compared on the low bound of other algorithm,the result shows that the new one is superior in the oretical senses.