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Mirko Hahn (hahnmanl.gov) Abstract: We apply the basic principles underlying combinatorial integral approximation methods for mixedinteger optimal control with ordinary differential equations in general, and the sumup rounding algorithm specifically, to optimization problems with partial differential equation (PDE) constraints. By doing so, we identify two possible generalizations that are applicable to problems involving PDE constraints with meshdependent integer variables, by minimizing errors in the PDE solution either pointwise or according to Hilbertlike norms and seminorms. We develop the theoretical underpinnings of these methods and formulate several variants. We apply these variants to 110 randomized instances of two test problems: 100 instances of a linearquadratic distributed control problem and 10 instances of a nonlinear topology optimization problem. We show that, especially in the case of Hilbertlike approximation methods, our approach can deliver highquality integer solutions in substantially less time than an exact branchandbound solver would take. Keywords: Mixedinteger programming, PDEconstrained programming, Combinatorial integral approximation, Decomposition methods Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization ) Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming ) Category 3: Applications  Science and Engineering (Optimization of Systems modeled by PDEs ) Citation: Hahn, Mirko and Sager, Sebastian. "Combinatorial Integral Approximation for MixedInteger PDEConstrained Optimization Problems", Argonne National Laboratory, Preprint ANL/MCSP90370118 Download: [PDF] Entry Submitted: 02/06/2018 Modify/Update this entry  
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