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math.OC2026
Regularization for Sparse Optimization: Consistency and Global Convergence
Yaohua Hu, Hao Wang, Xiaoqi Yang
The regularization method has a strong sparsity promoting capability in approaching sparse solutions of linear inverse problems and gained successful applicatio…
math.OC2025
Lipschitz continuity of solution multifunctions of extended regularization problems
Kaiwen Meng, Pengcheng Wu, Xiaoqi Yang
The Lasso and the basis pursuit in compressed sensing and machine learning are convex optimization problems with three parameters: the regularization scalar, the observation vector…
math.OC2025
Relative Well-Posedness of Truncated Constrained Systems Accompanied by Variational Calculus
Boris S. Mordukhovich, Pengcheng Wu, Xiaoqi Yang
The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general…