6 papers
Smoothness of Inertial Manifold for the Burgers Equation
Ziqi Niu, Xinhua Li, Chunyou Sun +1
This paper establishes a -smooth extension of the inertial manifold for the one-dimensional Burgers equation, which demonstrates that its long-time behavior c…
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…
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…
Stability Criteria and Calculus Rules via Conic Contingent Coderivatives in Banach Spaces
Boris S. Mordukhovich, Pengcheng Wu, Xiaoqi Yang
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of…
Variational Analysis of Kurdyka-Łojasiewicz Property, Exponent and Modulus
Minghua Li, Kaiwen Meng, Xiaoqi Yang
The Kurdyka-Łojasiewicz (KŁ) property, exponent and modulus have played a very important role in the study of global convergence and rate of convergence for optimal algorithms. In…
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…