6 papers · 1 filter
Stability results for regularized least-squares problems via generalized Hessian expressions and monotone generalized equations
Leo Smulansky, Tim Hoheisel, Tran T. A. Nghia
We study perturbation and stability properties of solution mappings associated with convex regularized least-squares problems. We first establish an implicit function theorem for g…
Isolated Calmness in Regularized Convex Optimization
Tran T. A. Nghia, Huy N. Pham
This paper studies the isolated calmness of the optimal solution mapping and the associated Lagrange system for regularized convex composite optimization problems. Several necessar…
Nonsmooth Newton methods with effective subspaces for polyhedral regularization
Tran T. A. Nghia, Nghia V. Vo, Khoa V. H. Vu
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated secon…
Stable Recovery of Regularized Linear Inverse Problems
Tran T. A. Nghia, Huy N. Pham, Nghia V. Vo
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that t…
Geometric characterizations of Lipschitz stability for convex optimization problems
Tran T. A. Nghia
In this paper, we mainly study tilt stability and Lipschitz stability of convex optimization problems. Our characterizations are geometric and fully computable in many important ca…
Lipschitz stability of least-squares problems regularized by functions with -cone reducible conjugates
Ying Cui, Tim Hoheisel, Tran T. A. Nghia +1
In this paper, we study Lipschitz continuity of the solution mappings of regularized least-squares problems for which the convex regularizers have (Fenchel) conjugates that are $\m…