Solving fuzzy variational inequalities over a compact set

This paper studies the fuzzy variational inequalities over a compact set. By using the tolerance approach, we show that solving such problems can be reduced to a semi-infinite programming problem. A relaxed cutting plane algorithm is proposed. In each iteration, we solve a finite optimization problem and add one more constraint. The proposed algorithm chooses a point at which the infinite constraints are violated to a degree rather than at which the violation is maximized. The iterative process ends when an optimal solution is identified. A convergence proof, under some mild conditions, is given. An efficient implementation based on the “entropic regularization” techniques is also included. To illustrate the solution procedure, a numerical example is provided.