Parallel Uzawa Method for Large-Scale Minimization of Partially Separable Functions

J. Koko ()
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J. Koko: Clermont Université, Université Blaise Pascal

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 1, No 10, 172-187

Abstract: Abstract A parallel Uzawa-type algorithm, for solving unconstrained minimization of large-scale partially separable functions, is presented. Using auxiliary unknowns, the unconstrained minimization problem is transformed into a (linearly) constrained minimization of a separable function.The augmented Lagrangian of this problem decomposes into a sum of partially separable augmented Lagrangian functions. To take advantage of this property, a Uzawa block relaxation is applied. In every iteration, unconstrained minimization subproblems are solved in parallel before updating Lagrange multipliers. Numerical experiments show that the speed-up factor gained using our algorithm is significant.

Keywords: Unconstrained minimization; Partially separable functions; Augmented Lagrangian (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0059-9

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