Mesh Independence of a Majorized ABCD Method for Sparse PDE-constrained Optimization Problems

Autor:	Song, Xiaoliang, Sun, Defeng, Toh, Kim-Chuan
Rok vydání:	2020
Předmět:	Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	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. Comment: arXiv admin note: substantial text overlap with arXiv:1709.00005, arXiv:1708.09094, arXiv:1709.09539
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.02118 Zobrazit plný text záznamu View this record from Arxiv