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Fast convergence of the simplified largest step path following algorithm

Abstract : Each master iteration of a simplified Newton algorithm for solving a system of equations starts by computing the Jacobian matrix and then uses this matrix in the computation of $ p $ Newton steps: the first of these steps is exact, and the other are called ``simplified''. In this paper we apply this approach to a large step path following algorithm for monotone linear complementarity problems. The resulting method generates sequences of objective values (duality gaps) that converge to zero with Q-order $ p+1$ in the number of master iterations, and with a complexity of $ O(\sqrt n L) $ iterations.
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https://hal.inria.fr/inria-00074242
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Submitted on : Wednesday, May 24, 2006 - 2:50:49 PM
Last modification on : Thursday, February 3, 2022 - 11:16:41 AM
Long-term archiving on: : Monday, April 5, 2010 - 12:06:56 AM

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  • HAL Id : inria-00074242, version 1

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Clovis C. Gonzaga, J. Frederic Bonnans. Fast convergence of the simplified largest step path following algorithm. [Research Report] RR-2433, INRIA. 1994. ⟨inria-00074242⟩

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