Abstract

SANCHEZ, WILMER; PEREZ, ROSANA  and  MARTINEZ, HÉCTOR J.. A global Jacobian smoothing algorithm for nonlinear complementarity problems. Integración - UIS [online]. 2021, vol.39, n.2, pp.191-215.  Epub Apr 18, 2022. ISSN 0120-419X.  https://doi.org/10.18273/revint.v39n2-20210004.

In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm.

MSC2010: 49M15, 90C06, 90C30.

Keywords : Nonlinear complementarity problems; complementarity function; generalized Newton methods; Jacobian smoothing method; global convergence; superlinear convergence; quadratic convergence.

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