论文标题
用于有效约束预处理的原始双投影算法
A primal dual projection algorithm for efficient constraint preconditioning
论文作者
论文摘要
我们考虑了一个线性迭代求解器，用于大规模约束二次最小化问题，例如在使用PDE中进行优化。通过原始的偶发投影（PDP）迭代，可以解释和分析作为商空间上的梯度方法，可以通过计算一系列约束替代问题，对可行的子空间的预测以及Lagrange乘数更新的序列来解决给定问题。作为主要应用程序，我们考虑了PDE的一类优化问题，其中PDP可以使用块三角形约束预处理使用投影的CG方法一起应用。数值实验显示出可靠和竞争性能，以实现弹性的最佳控制问题。
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gradient method on a quotient space, the given problem can be solved by computing sulutions for a sequence of constrained surrogate problems, projections onto the feasible subspaces, and Lagrange multiplier updates. As a major application we consider a class of optimization problems with PDEs, where PDP can be applied together with a projected cg method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity.
