No part of this Journal may be reproduced in any form, by print, photoprint, mi-croolm or any other means without written permission from Faculty of Technical The publication of Karmarkar's paper has resulted in intense research activity into interior{point algorithms for linear programming. Degeneracy is present in most real{life problems and has always been an important issue in linear progra...

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 ...

The computational difficulties that continue to plague decomposition algorithms, namely, “long-tail” convergence and numerical instabilities, have served to dampen enthusiasm about their computational effectiveness. The use of interior points of subproblems in decomposition procedures may have a significant role to play in alleviating such computational difficulties. Indeed, Dantzig-Wolfe decom...