Merit Functions for Complementarity and Related Problems: A Survey
Computational Optimization and Applications
Smoothing Newton and Quasi-Newton Methods for Mixed Complementarity Problems
Computational Optimization and Applications
Semismooth Newton Methods for Solving Semi-Infinite Programming Problems
Journal of Global Optimization
A Smoothing Newton Method for Semi-Infinite Programming
Journal of Global Optimization
Expected Residual Minimization Method for Stochastic Linear Complementarity Problems
Mathematics of Operations Research
Smoothing Newton method for NCP with the identification of degenerate indices
Journal of Computational and Applied Mathematics
Aggregate homotopy method for solving the nonlinear complementarity problem
ICICA'10 Proceedings of the First international conference on Information computing and applications
Computational Optimization and Applications
Solving the nonlinear complementarity problem via an aggregate homotopy method
International Journal of Computer Applications in Technology
A smoothing Broyden-like method for the mixed complementarity problems
Mathematical and Computer Modelling: An International Journal
Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization
Computational Optimization and Applications
Hi-index | 0.00 |
The nonlinear complementarity problem (NCP) can be reformulated as a system of semismooth equations by some NCP functions. A well-known NCP function is the Fischer-Burmeister function, which is a strongly semismooth function. It is smooth everywhere except at the origin. The generalized Newton direction of the system of semismooth equations formulated with the Fischer-Burmeister function is always a descent direction at a nonsolution point. The generalized Jacobian of the system is nonsingular under mild conditions. Efficient algorithms have been developed based upon these nice properties. In this paper, we define a class of NCP functions, called regular pseudo-smooth NCP functions, and show that they have these nice properties. Regular pseudosmooth NCP functions can be easily identified. They include the Fischer-Burmeister function, the Tseng-Luo NCP function family, and the Kanzow-Kleinmichel NCP function family. We give two new regular pseudo-smooth NCP function families: the ratio generated NCP function family and the C curve generated NCP function family. We then discuss the box constrained variational inequality problem (BVIP). We define a class of BVIP functions, called regular pseudo-smooth BVIP functions, and show that they have these nice properties too. We present three different approaches to generate regular pseudo-smooth BVIP functions from regular pseudo-smooth NCP functions. Globally and quadratically convergent generalized Newton methods are established for solving the NCP and the BVIP, based upon regular pseudo-smooth NCP and BVIP functions.