Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems

A P*-Nonlinear Complementarity Problem as a generalization of the P*-Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set

Long-Step Homogeneous Interior-Point Method for P*-Nonlinear Complementarity Problem

A P*-Nonlinear Complementarity Problem as a generalization of the P*Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set

Global convergence enhancement of classical linesearch interior point methods for MCPs

AbstractRecent works have shown that a wide class of globally convergent interior point methods may manifest a weakness of convergence. Failures can be ascribed to the procedure of linesearch along the Newton step. In this paper, we introduce a globally convergent interior point method which performs backtracking along a piecewise linear path. Theoretical and computational results show the effectiveness of our proposal

An infeasible interior-point method for the P∗P_*-matrix linear complementarity‎ ‎problem based on a trigonometric kernel function with full-Newton‎ ‎step

An infeasible interior-point algorithm for solving the‎ ‎$P_*$-matrix linear complementarity problem based on a kernel‎ ‎function with trigonometric barrier term is analyzed‎. ‎Each (main)‎ ‎iteration of the algorithm consists of a feasibility step and‎ ‎several centrality steps‎, ‎whose feasibility step is induced by a‎ ‎trigonometric kernel function‎. ‎The complexity result coincides with‎ ‎the best result for infeasible interior-point methods for‎ ‎$P_*$-matrix linear complementarity problem

Unified Analysis of Kernel-Based Interior-Point Methods for \u3cem\u3eP\u3c/em\u3e *(κ)-LCP

We present an interior-point method for the P∗(κ)-linear complementarity problem (LCP) that is based on barrier functions which are defined by a large class of univariate functions called eligible kernel functions. This class is fairly general and includes the classical logarithmic function and the self-regular functions, as well as many non-self-regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both long-step and short-step versions of the method for several specific eligible kernel functions. For some of them we match the best known iteration bounds for the long-step method, while for the short-step method the iteration bounds are of the same order of magnitude. As far as we know, this is the first paper that provides a unified approach and comprehensive treatment of interior-point methods for P∗(κ)-LCPs based on the entire class of eligible kernel functions