Degeneracy in interior point methods for linear programming

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 programming, especially in the Simplex Method. Degeneracy is also an important issue in Interior Point Methods (IPM's). However, the diiculties are diierent in the two methods. In this paper, we survey the various theoretical and practical issues related to degeneracy in IPM's for linear programming. We survey results which for the most part already appeared in the literature. Roughly speaking, we shall deal with four topics: the eeect of degeneracy on the convergence of IPM's, on the trajectories followed by the algorithms, the eeect of degeneracy in numerical performance, and on nding basic solutions.