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Paul Manns (paul.mannstubs.de) Abstract: Approximation algorithms like sumup rounding that allow to compute integervalued approximations of the continuous controls in a weak$^*$ sense have attracted interest recently. They allow to approximate (optimal) feasible solutions of continuous relaxations of mixedinteger control problems (MIOCPs) with integer controls arbitrarily close. To this end, they use compactness properties of the underlying state equation, a feature that is tied to the infinitedimensional vantage point. In this work, we consider a class of MIOCPs that are constrained by pointwise mixed statecontrol constraints. We show that a continuous relaxation that involves socalled vanishing constraints has beneficial properties for the described approximation methodology. Moreover, we complete recent work on a variant of the sumup rounding algorithm for this problem class. In particular, we prove that the observed infeasibility of the produced integervalued controls vanishes in an $L^\infty$sense with respect to the considered relaxation. Moreover, we improve the bound on the control approximation error to a value that is asymptotically tight. Keywords: Discrete approximations, error estimates, relaxations of mixed integer optimal control Category 1: Combinatorial Optimization (Approximation Algorithms ) Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming ) Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization ) Citation: Download: [PDF] Entry Submitted: 04/19/2018 Modify/Update this entry  
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