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

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 affine scaling algorithms generates an approximate solution (given a precision ϵ) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial of n, ln(1/ϵ) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen et al.