凸组合投影算法中的组合因子对算法效率的影响

在求解生产生活中各类实际问题的优化模型的算法研究中，投影梯度算法在解决凸约束最优化问题上一直被学者所重视．本文考虑凸组合投影算法求解凸约束最优化问题，在此凸组合投影算法中，由投影梯度法得到的点与上一步迭代点的凸组合得到新的迭代点．此算法不仅利用投影算法得到的点的信息而且也利用了前一步点的信息．进一步，通过数值实验分析凸组合算法的效率及凸组合因子对算法的影响．数值试验结果表明，这种凸组合算法总体比原来投影梯度法更稳定，而且这种凸组合算法在适当的凸组合因子下较投影梯度法收敛更快．

A Note on the Impact of the Convex Combination Factor of a Convex Combination Projection Algorithm

Many algorithms have been developed to solve optimization models which have wide-spread real-world applications. Among them, the gradient projection method for solving convex programs is one of the most noteworthy methodologies and has received much attention. In this paper, we consider a convex combination projection algorithm for solving convex programs. In the process of the convex combination projection algorithm, the new iterative point is updated based on the convex combination of the previous point and the point generated by the gradient projection method. Furthermore, we numerically analyze the efficiency and effectiveness of the convex combination projection algorithm and the impact of the convex combination factor on the algorithm. The numerical results show that the convex combination projection algorithm performs more stably than the gradient projection method and outperforms the gradient projection method when an appropriate convex combination factor is given.