Optimization and Engineering

, Volume 17, Issue 2, pp 359–384 | Cite as

A matrix-free augmented lagrangian algorithm with application to large-scale structural design optimization

  • Sylvain Arreckx
  • Andrew Lambe
  • Joaquim R. R. A. Martins
  • Dominique Orban
Article

Abstract

In many large engineering design problems, it is not computationally feasible or realistic to store Jacobians or Hessians explicitly. Matrix-free implementations of standard optimization methods—implementations that do not explicitly form Jacobians and Hessians, and possibly use quasi-Newton approximations—circumvent those restrictions, but such implementations are virtually non-existent. We develop a matrix-free augmented-Lagrangian algorithm for nonconvex problems with both equality and inequality constraints. Our implementation is developed in the Python language, is available as an open-source package, and allows for approximating Hessian and Jacobian information.We show that our approach solves problems from the CUTEr and COPS test sets in a comparable number of iterations to state-of-the-art solvers. We report numerical results on a structural design problem that is typical in aircraft wing design optimization. The matrix-free approach makes solving problems with thousands of design variables and constraints tractable, even when function and gradient evaluations are costly.

Keywords

Large-scale optimization Matrix-free optimization Structural optimization PDE-constrained optimization Augmented Lagrangian 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Sylvain Arreckx
    • 1
    • 2
  • Andrew Lambe
    • 3
  • Joaquim R. R. A. Martins
    • 4
  • Dominique Orban
    • 1
    • 2
  1. 1.GERADMontréalCanada
  2. 2.Department of Mathematics and Industrial EngineeringÉcole PolytechniqueMontréalCanada
  3. 3.University of Toronto Institute for Aerospace StudiesTorontoCanada
  4. 4.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA

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