The theoretical foundation of path-following methods is the performance analysis (damped) Newton step on class self-concordant functions. However, bounds available in literature and used design are not optimal. In this contribution we use optimal control theory to compute length method functions, as a function initial decrement, resulting worst-case decrease decrement. exact expressed terms sol...

Abstract We present a path-following interior-point algorithm for solving the weighted linear complementarity problem from implementation point of view. studied two variants, which differ only in method updating parameter characterizes central path. The was done C++ programming language and obtained numerical results prove efficiency proposed method.

Given a C1 path of systems of homogeneous polynomial equations ft, t ∈ [a, b] and an approximation xa to a zero ζa of the initial system fa, we show how to adaptively choose the step size for a Newton based homotopy method so that we approximate the lifted path (ft, ζt) in the space of (problems, solutions) pairs. The total number of Newton iterations is bounded in terms of the length of the li...

The inexact primal-dual interior point method which is discussed in this paper chooses a new iterate along an approximation to the Newton direction. The method is the Kojima, Megiddo, and Mizuno globally convergent infeasible interior point algorithm The inexact variation is shown to have the same convergence properties accepting a residual in both the primal and dual Newton step equation also ...

In this paper, an iterative method was considered for solving the absolute value equation (AVE). We suggest a two-step in which well-known Gauss quadrature rule is corrector step and generalized Newton taken as predictor step. The convergence of proposed established under some acceptable conditions. Numerical examples prove consistency capability new method.

This document proposes a Newton step graph-based model for Quadratic separable Problems (QSP). The Newton step is well suited for this kind of problems, but when the problem size grows the matrix-based QSP model will grow in a non linear manner. Furthermore, handling the constraints becomes the main problem as we have to select the right constraints in the different solution steps. When this ha...