5 papers · 1 filter
A Globally Convergent Newton Method for Nonsmooth Optimization in the absence of Smooth Surrogates
Tran T. A. Nghia, Nghia V. Vo, Khoa V. H. Vu
We propose a globally convergent Newton method for convex composite optimization problems with polyhedral regularizers. The method rests on the observation that the proximal gradie…
Isolated calmness of regularized linear inverse problems
Tran T. A. Nghia, Huy N. Pham, Nghia V. Vo +1
This paper studies the isolated calmness property of solution mappings arising from convex regularized linear inverse problems. We mainly establish a tangent-cone characterization…
Inexact DC Algorithms in Hilbert Spaces with Applications to PDE-Constrained Optimization
P. D. Khanh, V. V. H. Khoa, B. S. Mordukhovich +2
In this paper, we design and apply novel inexact adaptive algorithms to deal with minimizing difference-of-convex (DC) functions in Hilbert spaces. We first introduce I-ADCA, an in…
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…