Because of their versatility and robustness, numerical continuation or path following
methods have been finding ever wider use in scientific applications. Our aim here is to give …

Over the past fifteen years two new techniques have yielded extremely important
contributions toward the numerical solution of nonlinear systems of equations. This book …

This book was intended as an introduction to the topic of numerical continuation which
would be accessible to a readership of widely varying mathematical backgrounds. Realizing …

In this paper we continue the development of a theoretical foundation for efficient primal-
dual interior-point algorithms for convex programming problems expressed in conic form …

This note summarizes a report with the same title, where a study was carried out regarding a
unified approach, proposed by Kojima, Mizuno and Yoshise, for interior point algorithms for …

We describe several adaptive-step primal-dual interior point algorithms for linear
programming. All have polynomial time complexity while some allow very long steps in …

In this paper a unified treatment of algorithms is described for linear programming methods
based on the central path. This path is a curve along which the cost decreases, and that …

This paper presents a damped-Newton method for solving the linear complementarity
problem. The method is a specialization of a general Newton algorithm for solving B …

The main ideas of path following by predictor–corrector and piecewise-linear methods, and
their application in the direction of homotopy methods and nonlinear eigenvalue problems …

This paper presents a continuation method for linear complementarily problems based on a
new smooth equation formulation. In particular, the case of a linear complementarity …