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Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…

We design a new iterative algorithm, called REINFORCE-OPT, for solving a general type of optimization problems. This algorithm parameterizes the solution search rule and iteratively updates the parameter using a reinforcement learning (RL)…

We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…

This paper presents a novel method for recovering sparse vectors from linear models corrupted by Poisson noise. The contribution is twofold. First, an operator defined via the external division of two Bregman proximity operators is…

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…

We consider the problem of recovering an unknown effectively $(s_1,s_2)$-sparse low-rank-$R$ matrix $X$ with possibly non-orthogonal rank-$1$ decomposition from incomplete and inaccurate linear measurements of the form $y = \mathcal A (X) +…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…

Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…

This article aims to provide a comprehensive overview of sparse optimization, with a focus on both sparse signal recovery and sparse regularization techniques. We will begin by exploring the foundations of sparse optimization, delving into…

We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the…

Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the…

Sparseness is a useful regularizer for learning in a wide range of applications, in particular in neural networks. This paper proposes a model targeted at classification tasks, where sparse activity and sparse connectivity are used to…

We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics…

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…