A continuous deformation algorithm is proposed for solving a variational inequality probelm on a polytope K. The algorithm embeds the polytope K into K×[0,•) and starts by applying a variable dimension algorithm on K×{0} until an approximate solution is found on K×{0}. Then by tracing the path of solutions of a system of equations the algorithm virtually follows a path of approximate solution in K×[0,•). When the path in K×[0,•) returns to level 0, i.e., K×{0}, the variable dimension algorithm is again used until a new approximate solution is found on K×{0}. The set K×[0,•) is triangulated so that the approximate solution on the path improves the accuracy as the level increases. A contrivance for a practical implementation of the algorithm is proposed and tested for some test problems.
