G-2014-71
A matrix-free augmented Lagrangian algorithm with application to large-scale structural design optimization
Sylvain Arreckx, Andrew Lambe, Joaquim R.R.A. Martins, and Dominique Orban
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 - that do not explicitly form Jacobians and Hessians, and possibly use quasi-Newton derivative 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 it is competitive with existing state-of-the-art solvers on the CUTEr (Gould et al., 2003) and COPS (Bondarenko et al.) collections. We report numerical results on a structural design problem inspired by aircraft wing design. The matrix-free approach makes solving problems with thousands of design variables and constraints tractable, even if the function and gradient evaluations are costly.
Published September 2014 , 21 pages