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A Matrix-Free Augmented Lagrangian Algorithm with Application to Large-Scale Structural Design Optimization

TitleA Matrix-Free Augmented Lagrangian Algorithm with Application to Large-Scale Structural Design Optimization
Publication TypeJournal Articles
Year of Publication2016
AuthorsArreckx, S, Lambe, AB, Martins, JRRA, Orban, D
JournalOptimization and Engineering
Volume17
Pagination359–384
Date PublishedJune
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.

DOI10.1007/s11081-015-9287-9
Citation KeyArreckx2016