凸可行问题的平行近似次梯度投影算法

对凸可行问题提出了包括上松弛的平行近似次梯度投影算法和加速平行近似次梯度投影算法．与序列近似次梯度投影算法相比, 平行近似次梯度投影算法(每次迭代同时运用多个凸集的近似次梯度超平面上的投影)能够保证迭代序列收敛到离各个凸集最近的点． 上松弛的迭代技术和含有外推因子的加速技术的应用, 减少了数据存储量, 提高了收 敛速度. 最后在较弱的条件下证明了算法的收敛性, 数值实验结果验证了算法的有效性和优越性.

Parallel approximate subgradient projection algorithm for convex feasibility problem

In this paper, a relaxed parallel $\varepsilon$-subgradient projection algorithm which includes the over-relaxed case and an accelerated parallel $\varepsilon$-subgradient projection algorithm for solving convex feasibility problem (CFP) are presented. Compared with the previous subgradient projection algorithms, the algorithms presented in this paper use parallel process, i.e. in each iteration consider several approximation subgradient projections simultaneously. Algorithms adopt over-relaxed iterative process and accelerated technique. Hence, they can reduce the amounts of data storage and improve the convergence speed. And we also discuss the convergence of the methods under some mild conditions. Finally, the results of numerical experiment indicate that the algorithms are valid and have faster convergence speed than that of the algorithm in 18].