obstacle problem

On Solving Elliptic Obstacle Problems by Compact Abs-Linearization

  • Olga Weiß
  • Monika Weymuth
    • Categories Infinite Dimensional Optimization, Nonsmooth Optimization Tags , , , , , ,

    We consider optimal control problems governed by an elliptic variational inequality of the first kind, namely the obstacle problem. The variational inequality is treated by penalization which leads to optimization problems governed by a nonsmooth semi- linear elliptic PDE. The CALi algorithm is then applied for the efficient solution of these nonsmooth optimization problems. The … Read more

    On smooth relaxations of obstacle sets

  • Oliver Stein
  • Paul Steuermann
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , ,

    We present and discuss a method to relax sets described by finitely many smooth convex inequality constraints by the level set of a single smooth convex inequality constraint. Based on error bounds and Lipschitz continuity, special attention is paid to the maximal approximation error and a guaranteed safety margin. Our results allow to safely avoid … Read more