Mixed complementarity problems: Regularity, error bounds, and Newton-type methods

This paper is devoted to mixed complementarity problems (variational inequalities on a box). This class includes many important problem statements, for example, systems of equations, conventional complementarity problems, and Karush-Kuhn-Tucker systems. Error bounds and Newton-type methods for these problems are discussed. A new family of Newton-type methods is suggested that are globally convergent and the rate of local convergence is superlinear; these methods are superior to the available methods in certain respects. The presentation is accompanied by a detailed comparison of various relevant regularity conditions. Copyright © 2004 by MAIK "Nauka/ Interperiodica".