This note provides a simpliied proof concerning the paper \A Primal-Dual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix" by the same authors. In particular, we prove that Case II, one of the three cases in the method, can never occur.

Interior point methods proved to be efficient and robust tools for solving large–scale optimization problems. The standard infeasible–start implementations scope very well with wide variety of problem classes, their only serious drawback is that they detect primal or dual infeasibility by divergence and not by convergence. As an alternative, approaches based on skew–symmetric and self–dual refo...

Infeasible-interior-point paths are the main tools in interior-point methods for solving many kinds of optimization problems. These paths are usually parametrized by a penalty-parameter r ↓ 0 and further parameters describing their off-centrality and infeasiblilty. Starting with an early result of C. Witzgall et al. [12] in linear programming, this paper gives an overview on results concerning ...

Convex quadratic semidefinite programming (QSDP) has been widely applied in solving engineering and scientific problems such as nearest correlation problems and nearest Euclidean distance matrix problems. In this paper, we study an inexact primal-dual infeasible path-following algorithm for QSDP problems of the form: minX{12X • Q(X) + C •X : A(X) = b, X 0}, where Q is a self-adjoint positive se...