Abstract
Solution methods for very large scale optimization problems are addressed in this paper. Interior point methods are demonstrated to provide unequalled efficiency in this context. They need a small (and predictable) number of iterations to solve a problem. A single iteration of interior point method requires the solution of indefinite system of equations. This system is regularized to guarantee the existence of triangular decomposition. Hence the well-understood parallel computing techniques developed for positive definite matrices can be extended to this class of indefinite matrices. A parallel implementation of an interior point method is described in this paper. It uses object-oriented programming techniques and allows for exploiting different block-structures of matrices. Our implementation outperforms the industry-standard optimizer, shows very good parallel efficiency on massively parallel architecture and solves problems of unprecedented sizes reaching 109 variables.
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Supported by the Engineering and Physical Sciences Research Council of UK, EPSRC grant GR/R99683/01.
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Gondzio, J., Grothey, A. (2006). Direct Solution of Linear Systems of Size 109 Arising in Optimization with Interior Point Methods. In: Wyrzykowski, R., Dongarra, J., Meyer, N., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2005. Lecture Notes in Computer Science, vol 3911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11752578_62
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DOI: https://doi.org/10.1007/11752578_62
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