Decomposition Method for Lipschitz Stability of General LASSO-type Problems

Understand

This paper introduces a decomposition-based method to investigate the Lipschitz stability of solution mappings for general LASSO-type problems with convex data fidelity and $\ell_1$-regularization terms.

• The solution mappings are considered as set-valued mappings of the measurement vector and the regularization parameter.
• Based on the proposed method, we provide two regularity conditions for Lipschitz stability: the weak and strong conditions.
• The weak condition implies the Lipschitz continuity of solution mapping at the point in question, regardless of solution uniqueness.