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In this paper, we propose a novel adaptive sieving (AS) technique and anenhanced AS (EAS) technique, which are solver independent and could accelerateoptimization algorithms for solving large scale convex optimization problemswith intrinsic structured sparsity. We establish the finite convergenceproperty of the AS technique and the EAS technique with inexact solutions ofthe reduced subproblems. As an important application, we apply the AS techniqueand the EAS technique on the convex clustering model, which could acceleratethe state-of-the-art algorithm SSNAL by more than 7 times and the algorithmADMM by more than 14 times.

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