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.
翻译:我们考虑一个线性迭代求解器,用于解决大规模受线性限制的二次最小化问题,例如,在优化PDE中出现的问题。通过原始双投(PDP)迭代法(可以被解读和分析为商数空间的梯度法),特定的问题可以通过下列方法来解决:计算一系列受限制的代孕问题的隔热器,预测可行的子空间,以及Lagrange乘数更新。作为主要应用,我们考虑的是PDE的一类优化问题,即PDP可与使用块形三角约束先决条件的预测的克方法一起应用。数字实验显示,最佳控制的弹性问题具有可靠和竞争性的性能。