#
Fast Interior Point Solution of Quadratic Programming Problems
Arising from PDE-Constrained Optimization

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Technical Report ERGO-2015-013

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John W. Pearson and
J. Gondzio
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Abstract
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Interior point methods provide an attractive class of approaches
for solving linear, quadratic and nonlinear programming problems,
due to their excellent efficiency and wide applicability.
In this paper, we consider PDE-constrained optimization problems
with bound constraints on the state and control variables, and
their representation on the discrete level as quadratic programming
problems. To tackle complex problems and achieve high accuracy
in the solution, one is required to solve matrix systems of huge
scale resulting from Newton iteration, and hence fast and robust
methods for these systems are required. We present preconditioned
iterative techniques for solving a number of these problems using
Krylov subspace methods, considering in what circumstances one
may predict rapid convergence of the solvers in theory, as well
as the solutions observed from practical computations.

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Key words:
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Interior point methods, PDE-constrained optimization,
Krylov subspace method, Preconditioning, Schur complement.

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Text
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PDF ERGO-15-013.pdf.

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History:
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Written: December 11, 2015, revised February 18, 2017.

*Numerische Mathematik*
137 (2017) pp 959--999.