Properties of an augmented Lagrangian for design optimization
Properties of an augmented Lagrangian for design optimization
复制标题
用于设计优化的增广拉格朗日函数的属性
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Griewank
中科院分区：
文献类型：
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作者：
A. Hamdi;A. Griewank
我们考虑了设计优化的任务，其中的约束是一个状态方程，它只能用一个典型的相当缓慢地收敛的不动点求解器来求解。这一过程可以通过相应的伴随求解器来扩展，并且基于所得到的近似简化导数，还可以进行同时更新设计变量的优化迭代。为了协调三个迭代过程，我们使用了双增广的拉格朗日型的精确罚函数，该罚函数应该一致地减小。文中给出了Bratu问题的一个变种的数值实验。
We consider the task of design optimization, where the constraint is a state equation that can only be solved by a typically rather slowly converging fixed point solver. This process can be augmented by a corresponding adjoint solver, and based on the resulting approximate reduced derivatives, also an optimization iteration that updates the design variables simultaneously. To coordinate the three iterative processes, we use an exact penalty function of a doubly augmented Lagrangian type that should be consistently reduced. Some numerical experiments on a variant of the Bratu problem are presented.