Related papers: Revisiting $L_q(0\leq q<1)$ Norm Regularized Optim…
Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the L1/Lq norm with q > 1 is attractive in many applications of…
In this paper, we investigate a group sparse optimization problem via $\ell_{p,q}$ regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue…
In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, $L_{q}$ regularization with $q\in(0,1)$) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency.…
As a tractable approach, regularization is frequently adopted in sparse optimization. This gives rise to the regularized optimization, aiming at minimizing the $\ell_0$ norm or its continuous surrogates that characterize the sparsity. From…
We are concerned with a class of nonconvex and nonsmooth composite optimization problems, comprising a twice differentiable function and a prox-regular function. We establish a sufficient condition for the proximal mapping of a prox-regular…
In this paper, we consider nonconvex optimization problems with nonlinear equality constraints. We assume that the objective function and the functional constraints are locally smooth. To solve this problem, we introduce a linearized…
Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of…
We study a class of non-convex and non-smooth problems with \textit{rank} regularization to promote sparsity in optimal solution. We propose to apply the proximal gradient descent method to solve the problem and accelerate the process with…
Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…
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…
We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those…
Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the l1q norm with q>1 is attractive in many applications of…
This paper considers solving the unconstrained $\ell_q$-norm ($0\leq q<1$) regularized least squares ($\ell_q$-LS) problem for recovering sparse signals in compressive sensing. We propose two highly efficient first-order algorithms via…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
This paper concerns the composite problem of minimizing the sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. For this class of nonconvex and nonsmooth problems, by leveraging a practical inexactness…
We focus on solving the clustered lasso problem, which is a least squares problem with the $\ell_1$-type penalties imposed on both the coefficients and their pairwise differences to learn the group structure of the regression parameters.…
This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…