论文标题
用于稀疏PDE约束优化问题的主要ABCD方法的网格独立性
Mesh Independence of a Majorized ABCD Method for Sparse PDE-constrained Optimization Problems
论文作者
论文摘要
分析了希尔伯特空间中一种主要的加速块坐标下降（MABCD）方法，以通过其双重二元解决稀疏的PDE受限优化问题。研究了有限元近似方法。可以实现{MABCD}方法的偶数$ O（1/k^2）$迭代复杂性。基于收敛结果，我们通过确定无限的无限尺寸ABCD方法和有限的尺寸离散化具有相同的收敛性，并且MABCD方法的迭代次数几乎保持不变，我们证明了MABCD方法的网格大小$ h $的鲁棒性。
A majorized accelerated block coordinate descent (mABCD) method in Hilbert space is analyzed to solve a sparse PDE-constrained optimization problem via its dual. The finite element approximation method is investigated. The attractive $O(1/k^2)$ iteration complexity of {the mABCD} method for the dual objective function values can be achieved. Based on the convergence result, we prove the robustness with respect to the mesh size $h$ for the mABCD method by establishing that asymptotically the infinite dimensional ABCD method and finite dimensional discretizations have the same convergence property, and the number of iterations of mABCD method remains almost constant as the discretization is refined.
