This note points out an error in the local quadratic convergence proof of the predictorcorrector interior-point algorithm for solving the semidefinite linear complementarity problem based on the Alizadeh–Haeberly–Overton search direction presented in [M. Kojima, M. Shida, and S. Shindoh, SIAM J. Optim., 9 (1999), pp. 444–465]. Their algorithm is slightly modified and the local quadratic converg...

This paper proposes a globally convergent predictor-corrector infeasible-interiorpoint algorithm for the monotone semide nite linear complementarity problem using the AlizadehHaeberly-Overton search direction, and shows its quadratic local convergence under the strict complementarity condition.

This paper deals with the upwind finite volume method applied to the linear advection equation on a bounded domain and with natural boundary conditions. We introduce what we call the geometric corrector which is a sequence associated with every finite volume mesh in Rnd and every non vanishing vector a of Rnd. First we show that if the continuous solution is regular enough and if the norm of th...

We present a predictor{corrector non{interior path following algorithm for the monotone linear complementarity problem based on Chen{Harker{Kanzow{Smale smoothing techniques. Although the method is modeled on the interior point predictor{ corrector strategies, it is the rst instance of a non{interior point predictor{corrector algorithm. The algorithm is shown to be both globally linearly conver...

Abstract We study a predictor-corrector interior-point algorithm for solving general linear complementarity problems from the implementation point of view. analyze method proposed by Illés, Nagy and Terlaky [1] that extends published Potra Liu [2] to problems. A new determining step size corrector direction is presented. Using code implemented in C++ programming language, we can solve large-sca...

In the literature, various types of parallel methods for integrating nonsti initial-value problems for rst-order ordinary di erential equation have been proposed. The greater part of them are based on an implicit multistage method in which the implicit relations are solved by the predictor–corrector (or xed point iteration) method. In the predictor–corrector approach the computation of the comp...