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

被引:0
作者
Sylvain Arreckx
Andrew Lambe
Joaquim R. R. A. Martins
Dominique Orban
机构
[1] GERAD,Department of Mathematics and Industrial Engineering
[2] École Polytechnique,Department of Aerospace Engineering
[3] University of Toronto Institute for Aerospace Studies,undefined
[4] University of Michigan,undefined
来源
Optimization and Engineering | 2016年 / 17卷
关键词
Large-scale optimization; Matrix-free optimization; Structural optimization; PDE-constrained optimization; Augmented Lagrangian;
D O I
暂无
中图分类号
学科分类号
摘要
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.
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页码:359 / 384
页数:25
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