Related papers: Finding the Sparsest Vectors in a Subspace: Theory…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…
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 develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex…
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples. The time complexity of our…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…
In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…
We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We…