A closer look at consistent operator splitting and its extensions for topology optimization

Cameron Talischi, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is a classical structural design problem (e.g., compliance minimization and compliant mechanism design), parametrized by means of density functions, whose ill-posedness is addressed by introducing a Tikhonov regularization term. The proposed forward-backward splitting algorithm treats the constituent terms of the cost functional separately, which allows for suitable approximations of the structural objective. We will show that one such approximation, inspired by the reciprocal expansions underlying the optimality criteria method, improves the convergence characteristics and leads to an update scheme resembling the heuristic sensitivity filtering method. We also discuss a two-metric variant of the splitting algorithm that removes the computational overhead associated with bound constraints on the density field without compromising convergence and quality of optimal solutions. We present several numerical results and investigate the influence of various algorithmic parameters.

Original languageEnglish (US)
Pages (from-to)573-598
Number of pages26
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


  • Forward-backward splitting
  • Optimality criteria method
  • Tikhonov regularization
  • Topology optimization
  • Two-metric projection


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