Related papers: Maximal Solutions of Sparse Analysis Regularizatio…
This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…
The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the…
This paper studies the problem of exact localization of sparse (point or extended) objects with noisy data. The crux of the proposed approach consists of random illumination. Several recovery methods are analyzed: the Lasso, BPDN and the…
Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…
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 the original signal can be approximated linearly by optimal…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
Deep neural networks have become very popular in modeling complex nonlinear processes due to their extraordinary ability to fit arbitrary nonlinear functions from data with minimal expert intervention. However, they are almost always…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
In this paper, we study a maximization and a minimization problem associated with a Poisson boundary value problem. Optimal solutions in a set of rearrangements of a given function define stationary and stable flows of an ideal fluid in two…
We analyze a class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator. This construction, known as infimal postcomposition in convex analysis, is shown to encompass various of…
In this paper, we remark on the published paper "Treatment of Set-Valued Robustness via Separation and Scalarization" [1], which deals with the robust solution to an uncertain constrained set-valued optimization problem via scalarization…
We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We…
Motivated by practical applications, recent works have considered maximization of sums of a submodular function $g$ and a linear function $\ell$. Almost all such works, to date, studied only the special case of this problem in which $g$ is…
Owing to their statistical properties, non-convex sparse regularizers have attracted much interest for estimating a sparse linear model from high dimensional data. Given that the solution is sparse, for accelerating convergence, a working…
Based on the complete-lattice approach, a new Lagrangian duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum…
This paper studies the isolated calmness of the optimal solution mapping and the associated Lagrange system for regularized convex composite optimization problems. Several necessary and sufficient conditions for this property are…
Regularizing Deep Neural Networks (DNNs) is essential for improving generalizability and preventing overfitting. Fixed penalty methods, though common, lack adaptability and suffer from hyperparameter sensitivity. In this paper, we propose a…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…