Fast convergence of the simplified largest step path following algorithm
C. Gonzaga, Clovis ; Bonnans, J. Frederic
HAL, Report N°: RR-2433 / Harvested from HAL
Text on HAL
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.
Publié le : 1994-07-05
Classification:  SIMPLIFIED NEWTON METHOD,  CONVERGENCE OF ALGORITHMS,  LINEAR COMPLEMENTARITY PROBLEM,  PRIMAL-DUAL INTERIOR-POINT ALGORITHM,  [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH],  [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 
@article{Report N°: RR-2433,
     author = {C. Gonzaga, Clovis and Bonnans, J. Frederic},
     title = {Fast convergence of the simplified largest step path following algorithm},
     journal = {HAL},
     volume = {1994},
     number = {0},
     year = {1994},
     language = {en},
     url = {http://dml.mathdoc.fr/item/Report N°: RR-2433}
}

C. Gonzaga, Clovis; Bonnans, J. Frederic. Fast convergence of the simplified largest step path following algorithm. HAL, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/Report%20N%C2%B0:%20RR-2433/