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A Dimension Reduction Technique for Large-Scale Structured Sparse Optimization Problems with Application to Convex Clustering
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.
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