@article{SchielaStoeckleinWeiser, author = {Schiela, Anton and St{\"o}cklein, Matthias and Weiser, Martin}, title = {A primal dual projection algorithm for efficient constraint preconditioning}, series = {SIAM Journal on Scientific Computing}, volume = {43}, journal = {SIAM Journal on Scientific Computing}, number = {6}, doi = {10.1137/20M1380739}, pages = {A4095 -- A4120}, abstract = {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.}, language = {en} }