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Improved Regularity Assumptions for Partial Outer Convexification of Mixed-Integer PDE-Constrained Optimization problems

Paul Manns (paul.manns***at***tu-bs.de)
Christian Kirches (c.kirches***at***tu-bs.de)

Abstract: Partial outer convexification is a relaxation technique for MIOCPs being constrained by time-dependent differential equations. Sum-Up-Rounding algorithms allow to approximate feasible points of the relaxed, convexified continuous problem with binary ones that are feasible up to an arbitrarily small $\delta > 0$. We show that this approximation property holds for ODEs and semilinear PDEs under mild regularity assumptions on the nonlinearity and the solution trajectory of the PDE. In particular, requirements of differentiability and uniformly bounded derivatives on the involved functions from previous work are not necessary to show convergence of the method.

Keywords: Mixed-Integer Optimal Control with PDEs, Relaxations of Mixed-Integer Optimal Control, Regularity

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )


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Entry Submitted: 04/20/2018
Entry Accepted: 04/20/2018
Entry Last Modified: 03/25/2019

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