A power penalty approach to a discretized obstacle problem with nonlinear constraints

Abstract

A novel power penalty method is proposed to solve a nonlinear obstacle problem with nonlinear constraints arising from the discretization of an infinite-dimensional optimization problem. This approach is based on the formulation of a penalty equation approximating the mixed nonlinear complementarity problem arising from the Karush–Kuhn–Tucker conditions of the optimization problem. We show that the solution to the penalty equation converges to that of the complementarity problem with an exponential convergence rate depending on the parameters used in the penalty equation. Numerical experiments are performed to confirm the theoretical convergence rate established.