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The non-interior continuation methods for solving the \(P_0\) function nonlinear complementarity problem. (English) Zbl 1002.90072
Summary: We propose a new smoothing function that possesses a property not satisfied by the existing smoothing functions. Based on this smoothing function, we discuss the existence and continuity of the smoothing path for solving the \(P_0\) function Nonlinear Complementarity Problem (NCP). Using the characteristics of the new smoothing function, we investigate the boundedness of the iteration sequence generated by the non-interior continuation methods for solving the \(P_0\) function NCP under the assumption that the solution set of the NCP is nonempty and bounded. We show that the assumption that the solution set of the NCP is nonempty and bounded is weaker than those required by other continuation methods for solving the NCP.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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