论文标题
解决大规模优化问题的多分辨率方法
A Multiresolution approach to solve large-scale optimization problems
论文作者
论文摘要
通用优化技术可用于解决工程计算中的许多问题，尽管当自由度非常大时，它们的成本通常很高。我们描述了通过给定优化技术加快大规模优化问题解决方案解决方案的多级方法。通过将问题嵌入Harten的多分辨率框架（MRF）中，我们设置了一个程序，该程序是在计算有限的亚最佳解决方案序列后，该程序导致所需的解决方案，该序列解决了辅助优化问题，该问题涉及少量变量。对于具有平滑溶液的凸优化问题，我们证明了最佳溶液与每个亚最佳近似之间的距离与MRF中使用的插值技术的准确性有关，并分析了其与所提出算法的性能的关系。几个数值实验证实，我们的技术提供了一种计算高效的策略，该策略使最终用户可以在整个优化过程中将优化器和目标函数视为黑匣子。
General purpose optimization techniques can be used to solve many problems in engineering computations, although their cost is often prohibitive when the number of degrees of freedom is very large. We describe a multilevel approach to speed up the computation of the solution of a large-scale optimization problem by a given optimization technique. By embedding the problem within Harten's Multiresolution Framework (MRF), we set up a procedure that leads to the desired solution, after the computation of a finite sequence of sub-optimal solutions, which solve auxiliary optimization problems involving a smaller number of variables. For convex optimization problems having smooth solutions, we prove that the distance between the optimal solution and each sub-optimal approximation is related to the accuracy of the interpolation technique used within the MRF and analyze its relation with the performance of the proposed algorithm. Several numerical experiments confirm that our technique provides a computationally efficient strategy that allows the end user to treat both the optimizer and the objective function as black boxes throughout the optimization process.
