Improved penalty algorithm for mixed integer PDE constrained optimization problems

Optimal control problems including partial differential equation (PDE) as well integer constraints merge the combinatorial difficulties of programming and challenges related to large-scale systems resulting from discretized PDEs. So far, branch-and-bound framework has been most common solution strategy for such problems. In order provide an alternative approach, especially in a context, this article investigates penalization techniques. Taking inspiration well-known family existing exact penalty algorithms, novel improved algorithm is derived, whose key ingredients are basin hopping interior point method, both which specialized problem class. A thorough numerical investigation carried out standard stationary test problem. Extensions convection-diffusion nonlinear finally demonstrate versatility approach.