A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

Journal Article · Wed Jun 15 00:00:00 EDT 2005 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-005-0823-4· OSTI ID:21064216

Wang Yiju, E-mail: [e-mail]; Ma Fengming, E-mail: [e-mail]; Zhang Jianzhong ^[1]

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1. Institute of Operations Research, Qufu Normal University, Rizhao Shandong 276800 (China), E-mail: [e-mail]

In this paper the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone is reformulated as a system of nonsmooth equations. Based on this reformulation, the famous Levenberg-Marquardt (L-M) algorithm is employed to obtain its solution. Theoretical results that relate the stationary points of the merit function to the solution of the GNCP are presented. Under mild assumptions, we show that the L-M algorithm is both globally and superlinearly convergent.Moreover, a method to calculate a generalized Jacobian is given and numerical experimental results are presented.

• OSTI ID: 21064216
• Journal Information: Applied Mathematics and Optimization, Vol. 52, Issue 1; Other Information: DOI: 10.1007/s00245-005-0823-4; Copyright (c) 2005 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CONES
EQUATIONS
FUNCTIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS