Related papers: Trust-Region Methods for Sparse Relaxation

In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…

We consider the problem of recovering a complete (i.e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb{R}^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse.…

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…

In the context of inverse problems $\bf y = Ax$, sparse recovery offers a powerful paradigm shift by enabling the stable solution of ill-posed or underdetermined systems through the exploitation of structure, particularly sparsity. Sparse…

In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep…

We produce relaxation bounds on the diameter of arbitrary sections of the l1 ball in R^n. We use these results to test conditions for sparse recovery.

In this paper, we propose a novel low-tubal-rank tensor recovery model, which directly constrains the tubal rank prior for effectively removing the mixed Gaussian and sparse noise in hyperspectral images. The constraints of tubal-rank and…

We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…

In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular a Riemannian version of IHT is considered which significantly reduces…

Spectrum sensing is an important process in cognitive radio. A number of sensing techniques that have been proposed suffer from high processing time, hardware cost and computational complexity. To address these problems, compressive sensing…

We propose a trust-region stochastic sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with stochastic objectives and deterministic equality constraints. We consider a fully stochastic setting,…

In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often…

Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

In this paper, we consider the "foreach" sparse recovery problem with failure probability $p$. The goal of which is to design a distribution over $m \times N$ matrices $\Phi$ and a decoding algorithm $\algo$ such that for every…

This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low…

Adaptive trust-region methods attempt to maintain strong convergence guarantees without depending on conservative estimates of problem properties such as Lipschitz constants. However, on close inspection, one can show existing adaptive…

The trust-region (TR) method is renowned historically for its robustness in nonconvex problems and extraordinary numerical performance, but the study of its performance in convex optimization is somehow limited. This paper complements the…

We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computational efficiency and…