Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Approximation properties of sum-up rounding in the presence of vanishing constraints
HTML articles powered by AMS MathViewer

by Paul Manns, Christian Kirches and Felix Lenders HTML | PDF
Math. Comp. 90 (2021), 1263-1296 Request permission


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 $L^\infty$-sense with respect to the considered relaxation. Moreover, we improve the bound on the control approximation error to a value that is asymptotically tight.

Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2020): 90C59, 49M20, 49M25
  • Retrieve articles in all journals with MSC (2020): 90C59, 49M20, 49M25
Additional Information
  • Paul Manns
  • Affiliation: Institute for Mathematical Optimization, Technische Universität Braunschweig, 38106 Braunschweig, Germany
  • MR Author ID: 1201468
  • ORCID: 0000-0003-0654-6613
  • Email:
  • Christian Kirches
  • Affiliation: Institute for Mathematical Optimization, Technische Universität Braunschweig, 38106 Braunschweig, Germany
  • MR Author ID: 899522
  • ORCID: 0000-0002-3441-8822
  • Email:
  • Felix Lenders
  • Affiliation: ABB Corporate Research, ABB AG, 68526 Ladenburg, Germany.
  • ORCID: 0000-0003-3152-4221
  • Email:
  • Received by editor(s): December 14, 2017
  • Received by editor(s) in revised form: March 15, 2020, and September 25, 2020
  • Published electronically: February 18, 2021
  • Additional Notes: The first and second authors acknowledge funding by Deutsche Forschungsgemeinschaft through Priority Programme 1962, grants no KI1839/1-1 and KI1839/1-2. The second author acknowledges financial support by the German Federal Ministry of Education and Research, program “Mathematics for Innovations in Industry and Service”, grants no 05M2017-MoPhaPro, 05M2018-MOReNet, 05M2020-LEOPLAN, and program “IKT 2020: Software Engineering”, grant 01/S17089C-ODINE. The third author acknowledges funding by the German National Academic Foundation.
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 1263-1296
  • MSC (2020): Primary 90C59; Secondary 49M20, 49M25
  • DOI:
  • MathSciNet review: 4232224