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Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) Problems

Garmatter Dominik (dominik.garmatter***at***mathematik.tu-chemnitz.de)
Margherita Porcelli(margherita.porcelli***at***unibo.it)
Francesco Rinaldi(rinaldi***at***math.unipd.it)
Martin Stoll(martin.stoll***at***mathematik.tu-chemnitz.de)

Abstract: Optimal control problems including partial differential equation (PDE) as well as integer constraints combine the combinatorial difficulties of integer programming and large-scale systems resulting from discretizing the PDE. A common solution strategy for such a problem would be Branch-and-Bound. 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. Using a standard stationary model problem, the algorithm is then numerically investigated and compared with different solution strategies including a naive penalty approach and the Branch-and-Bound routine from CPLEX.

Keywords: mixed integer optimization, optimal control, PDE-constrained optimization, exact penalty methods

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Applications -- Science and Engineering (Control Applications )

Category 3: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Citation: arXiv:1907.06462

Download: [PDF]

Entry Submitted: 07/16/2019
Entry Accepted: 07/16/2019
Entry Last Modified: 07/16/2019

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