In this article, we study robust tensor completion by using transformed tensor singular value
decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier …

In this paper, we aim to prove the linear rate convergence of the alternating direction method
of multipliers (ADMM) for solving linearly constrained convex composite optimization …

Robust low-rank tensor completion plays an important role in multidimensional data analysis
against different degradations, such as Gaussian noise, sparse noise, and missing entries …

The sparse group Lasso is a widely used statistical model which encourages the sparsity
both on a group and within the group level. In this paper, we develop an efficient augmented …

Sdpnal+ is a Matlab software package that implements an augmented Lagrangian based
method to solve large scale semidefinite programming problems with bound constraints. The …

Clustering is a fundamental problem in unsupervised learning. Popular methods like K-
means, may suffer from poor performance as they are prone to get stuck in its local minima …

In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for
solving convex quadratic semidefinite programming (QSDP) problems with constraints …

This note serves two purposes. Firstly, we construct a counterexample to show that the
statement on the convergence of the alternating direction method of multipliers (ADMM) for …

In applying the level-set method developed in [E. Van den Berg and MP Friedlander, SIAM J.
Sci. Comput., 31 (2008), pp. 890--912] and [E. Van den Berg and MP Friedlander, SIAM J …

In this paper, we study the problem of low-rank tensor recovery from limited sampling with
noisy observations for third-order tensors. A tensor nuclear norm method based on a convex …