A variable transformation to box constraints for solving variational inequalities

For a class of linear variational inequalities resulting, e.g., from Signorini contact problems, a simple variable transformation (or synonymously a basis transformation) can be used to convert the linear inequality constraints into simple box constraints. This enables the use of efficient, stable and simple to implement iterative solvers. This manuscript shows how this variable transformation can be implicitly incorporated within an accelerated projected SOR scheme (APSOR) as well as the primal-dual active set method. In particular, some possible acceleration steps are proposed and the global convergence of the APSOR scheme is proven. Moreover, some implementational aspects are discussed and it is demonstrated that the accelerated projected symmetric SOR scheme is competitive to the locally quadratic converging primal-dual active set method.