homotopy method for solving ball-constrained variational inequalities

in this paper, we present a smoothing homotopy method for solving ball-constrained variational inequalities by utilizing a similar chen–harker–kanzow–smale function to smooth robinson’s normal equation. without any monotonicity condition on the defining map f, for the starting point chosen almost everywhere in rⁿ, the existence and convergence of the homotopy pathway are proven. numerical experiments illustrate that the method is feasible and effective.