Related papers: A new version of the convexification method for a …

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…

We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…

Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods,…

This paper is concerned with convergence of stochastic gradient algorithms with momentum terms in the nonconvex setting. A class of stochastic momentum methods, including stochastic gradient descent, heavy ball, and Nesterov's accelerated…

The aim of this paper is to deepen the convergence analysis of the scaled gradient projection (SGP) method, proposed by Bonettini et al. in a recent paper for constrained smooth optimization. The main feature of SGP is the presence of a…

The paper introduces the weighted convolution, a novel approach to the convolution for signals defined on regular grids (e.g., 2D images) through the application of an optimal density function to scale the contribution of neighbouring…

We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…

Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost.…

We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…

Classical analysis of convex and non-convex optimization methods often requires the Lipshitzness of the gradient, which limits the analysis to functions bounded by quadratics. Recent work relaxed this requirement to a non-uniform smoothness…

In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…

This paper considers an online proximal-gradient method to track the minimizers of a composite convex function that may continuously evolve over time. The online proximal-gradient method is inexact, in the sense that: (i) it relies on an…

In this paper, we present new second-order algorithms for composite convex optimization, called Contracting-domain Newton methods. These algorithms are affine-invariant and based on global second-order lower approximation for the smooth…

This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality…

This paper is concerned with the numerical solution to a 3D coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are associated with a single direction of an incident plane wave,…

This paper extends the classic theory of convex optimization to the minimization of functions that are equal to the negated logarithm of what we term as a sum-log-concave function, i.e., a sum of log-concave functions. In particular, we…

We are presenting a simple and numerical stable algorithm for the solution of the cone projection problem which is suitable for relative small data sets and for simulation purposes needed for convexity tests. Not even one pseudo-inverse…