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 …

Linear programming has been the dominant paradigm in optimization since Dantzig's
development of the simplex method in the 1940s. In 1984, the publication of a paper by …

The first comprehensive review of the theory and practice of one oftoday's most powerful
optimization techniques. The explosive growth of research into and development of …

This article provides a synopsis of the major developments in interior point methods for
mathematical programming in the last thirteen years, and discusses current and future …

As in many primal—dual interior-point algorithms, a primal—dual infeasible-interior-point
algorithm chooses a new point along the Newton direction towards a point on the central …

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 …

Based on Fischer's function, a new nonsmooth equations approach is presented for solving
nonlinear complementarity problems. Under some suitable assumptions, a local and Q …

This work, with its three parts, reviews the state-of-the-art of studies for the tensor
complementarity problem and some related models. In the first part of this paper, we have …

A noninterior continuation method is proposed for nonlinear complementarity problems. It
improves the noninterior continuation methods recently studied by Burke and Xu [Math …

In this paper, we propose a non-interior continuation method for solving generalized linear
complementarity problems (GLCP) introduced by Cottle and Dantzig. The method is based …