Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems

No part of this Journal may be reproduced in any form, by print, photoprint, microolm or any other means without written permission from Abstract This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu's scaled Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primal{dual aane scaling algorithms generates an approximate solution (given a precision) of the nonlinear complementarity problem in a nite number of iterations whose order is a polynomial of n, ln(1==) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in 13].