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

### B. Jansen, C. Roos, T. Terlaky, A. Yoshise

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 $\epsilon$) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial of $n$, $\ln(1/\epsilon)$ and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen, Roos and Terlaky for LCP.

Report 95-83, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.

Contact: t.terlaky@twi.tudelft.nl