修正的SQP型并行变量分配算法

A Modified SQP Parallel Variable Distribution Algorithm

Ferris和Mangasarian提出求解最优化问题的PVD(并行变量分配)算法,此算法是把变量分为主要变量和辅助变量,分配到p个处理机上,每个处理机除了负责更新本处理机的主要变量外,同时还沿着给定的方向更新辅助变量,使算法的鲁棒性和灵活性得到了很大的提高.该文基于文献[6]提出一种修正的SQP型PVD算法,构造其搜索方向是下降方向和可行方向的组合,并对此方向给予一个高阶修正,使此算法很好地防止Maratos效应发生,而且能够克服在求解子问题时出现约束不相容的情况.在合适的条件下,推导出此算法具有全局收敛性.

Ferris and Mangasarian proposed a PVD（parallel variable distribution） algorithm for solving optimization problems, which divides variables into primary and secondary variables groups. According to the algorithm, the variables are distributed among p parallel processors with each processor having the responsibility for updating its primary variables while allowing the remaining ＂secondary＂ variables to change in a restricted fashion along some easily com- putable directions, which enhances robustness and flexibility of the algorithm. In this paper, we present a modified SQP type PVD algorithm based on [6], whose search direction is a suitable combination of a descent direction and a feasible direction, and give a second-order revised for such a direction. This new algorithm is very effective in preventing Maratos effect from hap- pening, and avoid constraints in subproblem are inconsistent. We show the global convergence under some suitable conditions.