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A PRIMAL-DUAL PROJECTION ALGORITHM FOR EFFICIENT
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DOI：10.1137/20M1380739.png)
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Abstract
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We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with partial differential equations (PDEs). By a primal-dual projection (PDP) iteration, which can be interpreted and analyzed 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 conjugate gradient method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity.
Keywords:
iterative linear solvers
PDE constrained optimization
saddle point problems
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