论文标题
信任区域减少了基础Pascoletti-Serafini算法，用于多目标PDE约束参数优化
A trust region reduced basis Pascoletti-Serafini algorithm for multi-objective PDE-constrained parameter optimization
论文作者
论文摘要
在本文中，考虑了由椭圆化参数化的部分微分方程（PDE）控制的多目标参数优化问题。为了从数值上解决这些问题，应用了Pascoletti-Serafini标量，并通过增强的Lagrangian方法解决了获得的标量优化问题。但是，由于PDE约束，数值解决方案非常昂贵，因此使用还原基准（RB）方法来利用模型降低。 RB近似的质量是通过信任区域策略来确保不需要任何离线程序的，其中RB功能是在贪婪算法中计算的。此外，保证了所提出的方法的收敛性。数值示例说明了提出的解决方案技术的效率。
In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian method. However, due to the PDE constraints, the numerical solution is very expensive so that a model reduction is utilized by using the reduced basis (RB) method. The quality of the RB approximation is ensured by a trust-region strategy which does not require any offline procedure, where the RB functions are computed in a greedy algorithm. Moreover, convergence of the proposed method is guaranteed. Numerical examples illustrate the efficiency of the proposed solution technique.
