The authors studied in Preiß and Stoer (2003) the analyticity properties of infeasible-interior-point paths encountered in the context of semidefinite linear complementarity problems. It will be shown that these results allow for the design of infeasibleinterior-point methods of long-step type with an arbitrarily high order of local convergence for solving such problems.

We show that a modiication of the combined Phase I-Phase II interior-point algorithm for linear programming, due to Anstreicher, de Ghellinck and Vial, Fra-ley, and Todd, terminates in O(p nL) iterations from a suitable initial (interior but infeasible) solution. The algorithm either detects infeasibility, or approaches feasibility and optimality simultaneously, or generates a feasible primal-d...

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraints. New regularization techniques for Newton systems applicable to both symmetric positive de nite and symmetric inde nite systems are described. They transform the latter to quaside nite systems known to be strongly ...

This paper describes interior point methods for nonlinear programming endowed with infeasibility detection capabilities. The methods are composed of two phases, a main phase whose goal is to seek optimality, and a feasibility phase that aims exclusively at improving feasibility. A common characteristic of the algorithms is the use of a step-decomposition interior-point method in which the step ...

We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semideenite matrices. We present a theoretical convergence analysis, and show that the approach is very eecient for graph bisection problems, such as max-cut. The approach can also be applied to max-min eigenvalue problems.