A Dimension Reduction Technique for Large-Scale Structured Sparse Optimization Problems with Application to Convex Clustering
提出自适应筛选(AS)和增强自适应筛选(EAS)两种独立于求解器的降维技术，可加速大规模凸优化问题求解，在凸聚类模型中使Ssnal算法加速7倍以上、ADMM算法加速14倍以上。
In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and can accelerate optimization algorithms for solving large-scale convex optimization problems with intrinsic structured sparsity. We establish the finite convergence property of the AS and EAS techniques with inexact solutions of the reduced subproblems. As an important application, we apply the AS and EAS techniques to the convex clustering model, which can accelerate the state-of-the-art algorithm Ssnal by more than 7 times and the algorithm ADMM by more than 14 times.