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arXiv · 2012.01848

A primal dual projection algorithm for efficient constraint preconditioning

Anton Schiela·Matthias Stöcklein·Martin Weiser
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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.

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Anton Schiela, Matthias Stöcklein, Martin Weiser. 2020-12-04. A primal dual projection algorithm for efficient constraint preconditioning. https://arxiv.org/abs/2012.01848

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