Existence and Limiting Behavior of Trajectories Associatedwith P0-equations
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
SSVM: A Smooth Support Vector Machine for Classification
Computational Optimization and Applications
Journal of Optimization Theory and Applications
Complexity of a noninterior path-following method for the linear complementarity problem
Journal of Optimization Theory and Applications
A Smoothing Newton Method for General Nonlinear Complementarity Problems
Computational Optimization and Applications
Computational Optimization and Applications
Applications of smoothing methods in numerical analysis and optimization
Focus on computational neurobiology
epsilon-SSVR: A Smooth Support Vector Machine for epsilon-Insensitive Regression
IEEE Transactions on Knowledge and Data Engineering
Smoothing-type algorithm for solving linear programs by using an augmented complementarity problem
Applied Mathematics and Computation
Expected Residual Minimization Method for Stochastic Linear Complementarity Problems
Mathematics of Operations Research
A smoothing-type algorithm for solving system of inequalities
Journal of Computational and Applied Mathematics
A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems
Optimization Methods & Software
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
Computation of generalized differentials in nonlinear complementarity problems
Computational Optimization and Applications
SIAM Journal on Imaging Sciences
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A variational inequality problem with a mapping $g:\Re^n \to \Re^n$ and lower and upper bounds on variables can be reformulated as a system of nonsmooth equations $F(x)=0$ in $\Re^n$. Recently, several homotopy methods, such as interior point and smoothing methods, have been employed to solve the problem. All of these methods use parametric functions and construct perturbed equations to approximate the problem. The solution to the perturbed system constitutes a smooth trajectory leading to the solution of the original variational inequality problem. The methods generate iterates to follow the trajectory. Among these methods Chen--Mangasarian and Gabriel--Moré proposed a class of smooth functions to approximate $F$. In this paper, we study several properties of the trajectory defined by solutions of these smooth systems. We propose a homotopy-smoothing method for solving the variational inequality problem, and show that the method converges globally and superlinearly under mild conditions. Furthermore, if the involved function $g$ is an affine function, the method finds a solution of the problem in finite steps. Preliminary numerical results indicate that the method is promising.