Improved penalty algorithm for mixed integer PDE constrained optimization problems. (15th June 2022)

• Record Type: Journal Article
• Authors: Garmatter, Dominik; Porcelli, Margherita; Rinaldi, Francesco; Stoll, Martin
• Is Part Of: Computers & mathematics with applications. Volume 116(2022)
• Page Start: 2
• Page End: 14
• Publication Date: 2022-06-15
• Subjects: Mixed integer optimization -- Optimal control -- PDE-constrained optimization -- Exact penalty methods -- Interior point methods; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.11.004
• Languages: English
• ISSNs: 0898-1221

Abstract

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