Abstract
We present an approach for parallel space decomposition which facilitates minimization of sufficiently smooth non-linear functionals with or without constraints on the variables. The framework for the spatial decomposition unites existing approaches from parallel optimization, parallel variable distribution, and finite elements, Schwarz methods. Additive and multiplicative algorithms based on the spatial decomposition are described. Convergence theorems are also presented, from which convergence for the case of convex functionals, and hence linear least squares problems, follows immediately.
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© 1999 Springer Science+Business Media New York
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Frommer, A., Renaut, R.A. (1999). Parallel Space Decomposition for Minimization of Nonlinear Functionals. In: Yang, T. (eds) Parallel Numerical Computation with Applications. The Springer International Series in Engineering and Computer Science, vol 515. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5205-5_4
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DOI: https://doi.org/10.1007/978-1-4615-5205-5_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7371-1
Online ISBN: 978-1-4615-5205-5
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