Introducing the sequential linear programming level-set method for topology optimization

Peter D. Dunning*, H. Alicia Kim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

83 Citations (Scopus)
9 Downloads (Pure)


This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of non-level-set design variables.

Original languageEnglish
Pages (from-to)631-643
Number of pages13
JournalStructural and multidisciplinary optimization
Early online date30 Sep 2014
Publication statusPublished - Mar 2015


  • Level-set method
  • Topology optimization
  • Constraints
  • Sequential linear programming
  • structural topology
  • sensitivity-analysis
  • shape optimization
  • design
  • FEM


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