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Approximation Properties of Sum-up Rounding in the Presence of Vanishing Constraints
| Content Provider | Semantic Scholar |
|---|---|
| Author | Manns, Paul Kirches, Christian |
| Copyright Year | 2020 |
| Abstract | Approximation algorithms like sum-up rounding that allow to compute integer-valued approximations of the continuous controls in a weak∗ sense have attracted interest recently. They allow to approximate (optimal) feasible solutions of continuous relaxations of mixed-integer 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 infinite-dimensional vantage point. In this work, we consider a class of MIOCPs that are constrained by pointwise mixed state-control constraints. We show that a continuous relaxation that involves so-called vanishing constraints has beneficial properties for the described approximation methodology. Moreover, we complete recent work on a variant of the sum-up rounding algorithm for this problem class. In particular, we prove that the observed infeasibility of the produced integer-valued controls vanishes in an L∞-sense with respect to the considered relaxation. Moreover, we improve the bound on the control approximation error to a value that is asymptotically tight. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.optimization-online.org/DB_FILE/2018/04/6580.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
