Smoothing Levenberg–Marquardt method for general nonlinear complementarity problems under local error bound

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• 作者：Haodong Yu ; Dingguo Pu
• 关键词：Nonlinear complementarity problems ; Smoothing methods ; Levenberg&#x2013 ; Marquardt method ; Superliner convergence ; Local error bound
• 刊名：Applied Mathematical Modelling
• 出版年：2011
• 出版时间：March 2011
• 年：2011
• 卷：35
• 期：3
• 页码：1337-1348
• 全文大小：264 K

文摘

By using the F–B function and smoothing technique to convert the nonlinear complementarity problems to smoothing nonlinear systems, and introducing perturbation parameter μ_k into the smoothing Newton equation, we present a new smoothing Levenberg–Marquardt method for general nonlinear complementarity problems. For general mapping F, not necessarily a P₀ function, the algorithm has global convergence. Each accumulation point of the iterative sequence is at least a stationary point of the problem. Under the local error bound condition, which is much weaker than nonsingularity assumption or the strictly complementarity condition, we get the local superlinear convergence. Under some proper condition, quadratic convergence is also obtained.