基于牛顿法的并行优化算法

针对非线性数值优化问题，提出一种在分布式环境下的基于牛顿法的并行算法。引入松弛变量，将不等式约束转换为等式约束，利用广义拉格朗日乘子将约束优化问题转换为无约束子优化问题。为了并行地求解这些子优化问题，将Newton迭代法中的Hessian矩阵进行适当的分裂，采用简单迭代法求解Newton法中的线性方程组。在理论上对该算法进行了收敛性分析。在HP rx2600集群上进行的数值实验结果表明并行效率达90%以上。

Parallel optimization algorithm based on Newton method

This paper presented a parallel algorithm for solving nonlinear optimization problem on distributed-memory multi-computers.It converted optimization problem that contains inequality constraints to a problem with equality constraints by introducing slack variables.Replaced the equality constrained problem by a sequence of unconstrained sub-problems by augmented Lagrangian method.To parallelly solve the nonlinear unconstrained sub-optimization problem,properly splitted Hessian matrix in Newton method.It solve...