【作者】 黄利国；

【导师】 贺国平；

【作者基本信息】 山东科技大学 ， 运筹学与控制论， 2006， 硕士

【摘要】 本文利用Ferris[1]等人于1994年提出的PVD算法框架及Fukushima于1998年在[3]中提出的无约束最优化问题的PVT算法框架，对约束最优化问题的PVD算法和PVT算法进行了研究。 第一章主要介绍了有关并行优化算法研究的现状、发展方向及一些常用并行环境和软件。 第二、三章，我们研究了含特殊约束最优化问题的PVD算法和PVT算法。在第二章，我们对约束具有块可分结构最优化问题的PVD算法进行了研究，利用序列线性方程组方法对PVD子问题进行求解，给出了一个QP-free型PVD算法，它简化了PVD子问题的求解过程。第三章，我们对含边界约束的PVT算法进行了研究，给出了求解边界约束优化问题的PVT可行算法。 在第四章中我们研究了PVT算法和PVD算法在Rosen梯度投影对偶算法中的应用，给出了求解凸约束优化问题的部分并行的新算法。更多还原

【Abstract】 In this paper, based on the parallel variable distribution(PVD) algorithm proposed by Ferris and Mangasarian in 1994 and the parallel variable transformation(PVT) algorithm presented by Fukushima in 1998, we proposed two PVD algorithms and three PVT algorithms, respectively for special structure nonlinear optimization problems.Firstly, we introduced the development and the current research situations of the parallel optimization algorithms as well as some parallel environments and optimization softwares.In the second and third chapter, we mainly concerned PVD algorithms and PVT algorithms for constrained optimization problem. In the second chapter, not assuming that the constraints are convex, but assuming with block-separable structure, we suggested that each PVD subproblem can be solved inexactly by solving three systems of linear equations with the same coefficient matrix. This made the computation much less than that by solving a sequential quadratic programming(SQP) for every PVD subproblem presented by Sagastizab-al and solodov in 2002. In the third chapter, we concerned PVT algorithms for bound constrained optimization problem and proposed two feasible PVT algorithms.In the fourth chapter, combined with parallel algorithms and Rosen gradient projection algorithm, we proposed two new partial parallel algorithms for solving convex constrained optimization.更多还原