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Perturbation Homotopy Method for Solving Variational Inequalities with General Constraints on an Unbounded Set

Xiaona Fan, Furong Gao, Tingtin Xu


In this paper, a new homotopy method is proposed for solving the variational inequality problem (VIP) with both equality and inequality constraints on an unbounded set. To enlarge the scope of initial points, we give a suitable perturbation on the equality constraint. Under certain nonmonotone condition, for almost all initial points in the interior of only inequality constraint set, existence and convergence of a smooth homotopy pathway to a solution of VIP are proved. Preliminary numerical experiments indicate that the method is feasible.


variational inequality, combined homotopy method, unbounded set, global convergence.

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