NONCONVEX WIENER-HOPF EQUATIONS AND VARIATIONAL INEQUALITIES

We consider the problem of solving the nonconvex Wiener-Hopf equations on the prox-regular sets. Using the projection technique, we show that the nonconvex Wiener-Hopf equations are equivalent to the strongly nonlinear nonconvex variational inequalities. This equivalence is used to suggest several iterative methods for solving the strongly nonlinear nonconvex variational inequalities. We also discuss the convergence of these new iterative methods under suitable conditions. Several special cases are also considered.