Abstract
In this work we describe three sequential algorithms and their parallel counterparts for solving nonlinear systems, when the Jacobian matrix is symmetric and positive definite. This case appears frequently in unconstrained optimization problems. Two of the three algorithms are based on Newton’s method. The first solves the inner iteration with Cholesky decomposition while the second is based on the inexact Newton methods family, where a preconditioned CG method has been used for solving the linear inner iteration. In this latter case and to control the inner iteration as far as possible and avoid the oversolving problem, we also parallelized several forcing term criteria and used parallel preconditioning techniques. The third algorithm is based on parallelizing the BFGS method. We implemented the parallel algorithms using the SCALAPACK library. Experimental results have been obtained using a cluster of Pentium II PC’s connected through a Myrinet network. To test our algorithms we used four different problems. The algorithms show good scalability in most cases.
Work supported by Spanish CICYT. Project TIC 2000-1683-C03-03.
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Peinado, J., Vidal, A.M. (2005). Three Parallel Algorithms for Solving Nonlinear Systems and Optimization Problems . In: Daydé, M., Dongarra, J., Hernández, V., Palma, J.M.L.M. (eds) High Performance Computing for Computational Science - VECPAR 2004. VECPAR 2004. Lecture Notes in Computer Science, vol 3402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11403937_49
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DOI: https://doi.org/10.1007/11403937_49
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