Study Of Parallel Optimization Algorithms

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.