A family of NCP functions and a descent method for the nonlinear complementarity problem
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Information Sciences: an International Journal
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
Numerical comparisons of two effective methods for mixed complementarity problems
Journal of Computational and Applied Mathematics
A new class of penalized NCP-functions and its properties
Computational Optimization and Applications
Neural networks for solving second-order cone constrained variational inequality problem
Computational Optimization and Applications
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This paper is a follow-up of the work [Chen, J.-S.: J. Optimiz. Theory Appl., Submitted for publication (2004)] where an NCP-function and a descent method were proposed for the nonlinear complementarity problem. An unconstrained reformulation was formulated due to a merit function based on the proposed NCP-function. We continue to explore properties of the merit function in this paper. In particular, we show that the gradient of the merit function is globally Lipschitz continuous which is important from computational aspect. Moreover, we show that the merit function is SC 1 function which means it is continuously differentiable and its gradient is semismooth. On the other hand, we provide an alternative proof, which uses the new properties of the merit function, for the convergence result of the descent method considered in [Chen, J.-S.: J. Optimiz. Theory Appl., Submitted for publication (2004)].