A truncated Newton method with nonmonotone line search for unconstrained optimization
Journal of Optimization Theory and Applications
Avoiding the Maratos effect by means of a nonmonotone line search I. general constrained problems
SIAM Journal on Numerical Analysis
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
A non-interior-point continuation method for linear complementarity problems
SIAM Journal on Matrix Analysis and Applications
A class of smoothing functions for nonlinear and mixed complementarity problems
Computational Optimization and Applications
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
A Comparison of Large Scale Mixed Complementarity Problem Solvers
Computational Optimization and Applications
Mathematics of Operations Research
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
Computational Optimization and Applications
Weak Univalence and Connectedness of Inverse Images of Continuous Functions
Mathematics of Operations Research
On Homotopy-Smoothing Methods for Box-Constrained Variational Inequalities
SIAM Journal on Control and Optimization
Journal of Optimization Theory and Applications
Regularization of P0-Functions in Box Variational Inequality Problems
SIAM Journal on Optimization
SIAM Journal on Optimization
Jacobian Smoothing Methods for Nonlinear Complementarity Problems
SIAM Journal on Optimization
On the nonmonotone line search
Journal of Optimization Theory and Applications
A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
SIAM Journal on Optimization
Sub-quadratic convergence of a smoothing Newton algorithm for the P0– and monotone LCP
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Smoothing-type algorithm for solving linear programs by using an augmented complementarity problem
Applied Mathematics and Computation
A smoothing-type algorithm for solving system of inequalities
Journal of Computational and Applied Mathematics
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
A nonmonotone smoothing-type algorithm for solving a system of equalities and inequalities
Journal of Computational and Applied Mathematics
A non-interior continuation algorithm for the CP based on a generalized smoothing function
Journal of Computational and Applied Mathematics
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The smoothing-type algorithm has been a powerful tool for solving various optimization problems. In order to improve the numerical results of the algorithm, the nonmonotone line search technique has been used when the algorithm is implemented. However, the theoretical analysis is based on the algorithm with some monotone line search. In this paper, based on the smoothed Kanzow-Kleinmichel NCP function, we propose a smoothing Newton algorithm for solving the nonlinear complementarity problem with a new nonmonotone line search. We show that the nonmonotone algorithm is globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are also reported.