A relaxed projection method for variational inequalities
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Mathematical Programming: Series A and B
Normal maps inducted by linear transformations
Mathematics of Operations Research
A globally convergent Newton method for solving strongly monotone variational inequalities
Mathematical Programming: Series A and B
NE/SQP: a robust algorithm for the nonlinear complementarity problem
Mathematical Programming: Series A and B
A continuation method for monotone variational inequalities
Mathematical Programming: Series A and B
Implementation of a continuation method for normal maps
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem
Nonlinear Analysis: Theory, Methods & Applications
A homotopy continuation method for solving normal equations
Mathematical Programming: Series A and B
Homotopy method for solving variational inequalities
Journal of Optimization Theory and Applications
A New Projection Method for Variational Inequality Problems
SIAM Journal on Control and Optimization
Exceptional families and existence theorems for variational inequality problems
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
Improvements of some projection methods for monotone nonlinear variational inequalities
Journal of Optimization Theory and Applications
Homotopy Methods for Solving Variational Inequalities in Unbounded Sets
Journal of Global Optimization
Optimization Methods & Software
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In this paper, based on the Robinson's normal equation and the smoothing projection operator, a smoothing homotopy method is presented for solving variational inequality problems on polyhedral convex sets. We construct a new smoothing projection operator onto the polyhedral convex set, which is feasible, twice continuously differentiable, uniformly approximate to the projection operator, and satisfies a special approximation property. It is computed by solving nonlinear equations in a neighborhood of the nonsmooth points of the projection operator, and solving linear equations with only finite coefficient matrices for other points, which makes it very efficient. Under the assumption that the variational inequality problem has no solution at infinity, which is a weaker condition than several well-known ones, the existence and global convergence of a smooth homotopy path from almost any starting point in $$R^n$$ are proven. The global convergence condition of the proposed homotopy method is same with that of the homotopy method based on the equivalent KKT system, but the starting point of the proposed homotopy method is not necessarily an interior point, and the efficiency is more higher. Preliminary test results show that the proposed method is practicable, effective and robust.