Smoothing methods for convex inequalities and linear complementarity problems
Mathematical Programming: Series A and B
A class of smoothing functions for nonlinear and mixed complementarity problems
Computational Optimization and Applications
Some Noninterior Continuation Methods for LinearComplementarity Problems
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
Improving the convergence of non-interior point algorithms for nonlinear complementarity problems
Mathematics of Computation
Computational Optimization and Applications
A new approach to continuation methods for complementarity problems with uniform P-functions
Operations Research Letters
Computational Optimization and Applications
Computational Optimization and Applications
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We propose a new smoothing method using CHKS-functions for solving linear complementarity problems. While the algorithm in K. Hotta, M. Inaba, and A. Yoshise (Discussion Paper Series 807, University of Tsukuba, Ibaraki 305, Japan, 1998) uses a quite large neighborhood, our algorithm generates a sequence in a relatively narrow neighborhood and employs predictor and corrector steps at each iteration. A complexity bound for the method is also provided under the assumption that (i) the problem is monotone, (ii) a feasible interior point exists, and (iii) a suitable initial point can be obtained. As a result, the bound can be improved compared to the one in Hotta et al. (1998). We also mention that the assumptions (ii) and (iii) can be removed theoretically as in the case of interior point method.