# Fast convergence of the simplified largest step path following algorithm

1 PROMATH - Mathematical Programming
Inria Paris-Rocquencourt
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
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### Identifiers

• HAL Id : inria-00074242, version 1

### Citation

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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