Related papers: Solving the OSCAR and SLOPE Models Using a Semismo…

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…

We introduce a new estimator for the vector of coefficients $\beta$ in the linear model $y=X\beta+z$, where $X$ has dimensions $n\times p$ with $p$ possibly larger than $n$. SLOPE, short for Sorted L-One Penalized Estimation, is the…

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant positive linear dependence…

Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…

Sparse optimization has seen its advances in recent decades. For scenarios where the true sparsity is unknown, regularization turns out to be a promising solution. Two popular non-convex regularizations are the so-called $L_0$ norm and…

We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is…

The hard margin loss function has been at the core of the support vector machine (SVM) research from the very beginning due to its generalization capability.On the other hand, the cardinality constraint has been widely used for feature…

This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical…

In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic…

We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty…

Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$…

Nonlinearly constrained nonconvex and nonsmooth optimization models play an increasingly important role in machine learning, statistics and data analytics. In this paper, based on the augmented Lagrangian function we introduce a flexible…

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class…

Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the…