Abstract
AbstractIn this paper, we propose a Jacobian smoothing inexact Newton-type algorithm for solving the nonlinear complementarity problem by reformulating it as a system of nonlinear equations. We show that the algorithm converges up to q-quadratically and present numerical experiments that show its good local performance. In order to compare in terms of time our algorithm with other known algorithms, we introduce a new normalized measurement that we call time index.
Publisher
Springer Science and Business Media LLC
Reference35 articles.
1. Anitescu M, Cremer J, Potra F (1997) On the existence of solutions to complementarity formulations of contact problems with friction. Complement Var Probl State Art 92:12
2. Arenas F, Marínez HJ, Pérez R (2014) Redefining the Kanzow complementarity function. Rev Cienc 18(2):111–122
3. Arenas F, Martínez H, Pérez R (2020) A local Jacobian smoothing method for solving nonlinear complementarity problems. Univ Sci 25:149–174. https://doi.org/10.11144/Javeriana.SC25-1.aljs
4. Birgin E, Krejić N, Martínez JM (2003) Globally convergent inexact quasi-Newton methods for solving nonlinear systems. Numer Algorithms 32:249–260. https://doi.org/10.1023/A:1024013824524
5. Broyden C, Dennis J Jr, Moré J (1973) On the local and superlinear convergence of quasi-Newton methods. IMA J Appl Math 12:223–245. https://doi.org/10.1093/imamat/12.3.223