伪单调均衡问题的一种加速投影算法

介绍了求解均衡问题的几类算法,并针对收敛性证明需要Lipschitz连续性条件的问题,提出了一种加速投影算法.该算法首先由辅助问题原理和Armijo型线搜索得到一个预估点并以此构造一个超平面,进一步通过选择适当步长和减小投影域使得算法产生的序列快速收敛,从而实现加速投影的目的.最后,在双重函数f伪单调且不需要Lipschitz连续的条件下,证明了该算法产生的迭代序列全局收敛到伪单调均衡问题的解.

Accelerating Projection Algorithm for Pseudomonotone Equilibrium Problems

Several algorithms for solving equilibrium problems were introduced.Aiming at the problem that the convergence proof should be under the Lipschitz continuity condition,an accelerating projection algorithm was proposed.The algorithm adopts the auxiliary problem principle and the Armijo-type line-search technique to get an estimate point.According to the estimate point,a hyperplane was constructed.Through selecting an appropriate step length and reducing the projection domain,the sequence generated by the algorithm gained a fast speed constringency,which realizes the purpose of accelerating the projection.Finally,under some suitable conditions (without Lipschitz-type continuous condition),the global convergence of the sequence was proved.