关键词: 约束优化, 变分不等式, 投影梯度法, 凸组合算法

Abstract: 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.

Key words: constraint programming, variational inequality, gradient projection method, convex combination algorithm