Advances in Computational Mathematics

, Volume 43, Issue 5, pp 945–972 | Cite as

Multiobjective PDE-constrained optimization using the reduced-basis method

  • L. Iapichino
  • S. Ulbrich
  • S. VolkweinEmail author


In this paper the reduced basis (RB) method is applied to solve quadratic multiobjective optimal control problems governed by linear parametrized variational equations. These problems often arise in applications, where the quality of the system behavior has to be measured by more than one criterium. The weighted sum method is exploited for defining scalar-valued linear-quadratic optimal control problems built by introducing additional optimization parameters. The optimal controls corresponding to specific choices of the optimization parameters are efficiently computed by the RB method. The accuracy is guaranteed by an a-posteriori error estimate. An effective sensitivity analysis allows to further reduce the computational times for identifying a suitable and representative set of optimal controls.


Multiobjective PDE-constrained optimization Weighted sum method Reduced basis method A-posteriori error Sensitivity analysis 

Mathematics Subject classification (2010)

35J20 49N10 65N30 90C29 


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Precision and Microsystems EngineeringDelft University of TechnologyDelftThe Netherlands
  2. 2.Department of MathematicsDarmstadt University of TechnologyDarmstadtGermany
  3. 3.Department of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany

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