并行求解约束优化问题的QP-free型算法  

A parallel algorithm based on QP-free for constrained optimizations

作　　者：黄利国[1] 孙莉[2] 韩丛英[3] 

机构地区：[1]滨州学院数学与信息科学系,山东滨州256603 [2]山东农业大学信息科学与工程学院,山东泰安271018 [3]山东科技大学信息科学与工程学院,山东青岛266510

出　　处：《纯粹数学与应用数学》2011年第1期63-68,80,共7页Pure and Applied Mathematics

基　　金：山东省科技攻关项目(2009GG10001012);滨州学院科研基金(BZXYL201005)

摘　　要：针对约束块可分的最优化问题,引入序列线性方程组方法和有效集策略,提出了一个求解约束块可分优化问题的QP-free型并行变量分配(PVD)算法.算法中用三个系数具有对称结构的线性方程组来代替PVD算法中的二次规划问题以求解线搜索方向,避免了约束不相容,减小了计算量.并且算法不要求约束是凸的.最后证明了QP-free型PVD算法的全局收敛性.In this paper, a parallel variable distribution algorithm based on QP-free is proposed to solve constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation and active set. The feature of the method is that only the systems of linear equations with symmetrical structure are solved in each iteration, other than the quadratic programming, which avoids the constraints in compatible and decreases the amount of computations. In addition, the constraints aren’t necessarily convex. Global convergence is obtained under certain conditions.

关 键 词：序列二次规划 并行变量分配 全局收敛性 序列线性方程组 有效集 

分 类 号：O221[理学—运筹学与控制论]