A Regularization Newton Method for Solving Nonlinear Complementarity Problems

Journal Article · Mon Nov 15 04:00:00 EST 1999 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S002459900128· OSTI ID:21067537

In this paper we construct a regularization Newton method for solving the nonlinear complementarity problem (NCP(F )) and analyze its convergence properties under the assumption that F is a P{sub 0} -function. We prove that every accumulation point of the sequence of iterates is a solution of NCP(F ) and that the sequence of iterates is bounded if the solution set of NCP(F ) is nonempty and bounded. Moreover, if F is a monotone and Lipschitz continuous function, we prove that the sequence of iterates is bounded if and only if the solution set of NCP(F ) is nonempty by setting t=1/2 , where t element of [1/2,1] is a parameter. If NCP(F) has a locally unique solution and satisfies a nonsingularity condition, then the convergence rate is superlinear (quadratic) without strict complementarity conditions. At each step, we only solve a linear system of equations. Numerical results are provided and further applications to other problems are discussed.

• OSTI ID: 21067537
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 40; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONVERGENCE
EQUATIONS
FUNCTIONS
MATHEMATICAL SOLUTIONS
NEWTON METHOD
NONLINEAR PROBLEMS