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The elastic net penalty is frequently employed in high-dimensional statistics for parameter regression and variable selection. It is particularly beneficial compared to lasso when the number of predictors greatly surpasses the number of…
We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem.…
As one of the most plausible convex optimization methods for sparse data reconstruction, $\ell_1$-minimization plays a fundamental role in the development of sparse optimization theory. The stability of this method has been addressed in the…
Compressed Sensing using $\ell_1$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network…
We propose an iterative algorithm for the minimization of a $\ell_1$-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices…
In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including…
We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework…
We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take…
Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we developed an efficient algorithm for the sparsity promoting…
The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…
Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…
We study sparse signal recovery from noisy linear observations using nonconvex log-sum regularization. The log-sum penalty reduces the shrinkage bias of $\ell_1$ regularization and more closely approximates the $\ell_0$ regularization, but…
In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…