Vietnam Journal of Mathematics

, Volume 46, Issue 4, pp 825–836 | Cite as

New Results for the Handling of Additional Equality Constraints in One-Shot Optimization

  • Andrea WaltherEmail author
  • Lisa Kusch
  • Nicolas R. Gauger


The one-shot approach is often applied for design optimization tasks involving a slowly converging Newton-like solver for the underlying partial differential equations. The state solver is augmented with an adjoint solver to obtain reduced derivatives for an optimization step. The idea of the one-shot approach is to simultaneously pursue state and adjoint feasibility as well as optimality by using a suitable design space preconditioner. In various applications, further equality constraints additional to the partial differential equations describing the state are required. The one-shot approach can be extended to deal with additional equality constraints by introducing an additional update formula for the corresponding constraint multipliers. The choice of a suitable preconditioner for the design update as well as for the constraint multiplier update is important to achieve bounded retardation. We derive conditions for the preconditioners of the extended one-shot approach and propose a suitable preconditioner for the multiplier updates for the additional constraints.


One-shot optimization Design optimization Equality constraints Preconditioner 

Mathematics Subject Classification (2010)

65H05 49M05 65F08 


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Institute of MathematicsPaderborn UniversityPaderbornGermany
  2. 2.Chair for Scientific ComputingTechnische Universität KaiserslauternKaiserslauternGermany

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