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The core of many approaches for the resolution of variational inverse problems arising in signal and image processing consists of promoting the sought solution to have a sparse representation in a well-suited space. A crucial task in this…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
In this paper we consider a distributed convex optimization problem over time-varying networks. We propose a dual method that converges R-linearly to the optimal point given that the agents' objective functions are strongly convex and have…
We investigate a class of general combinatorial graph problems, including MAX-CUT and community detection, reformulated as quadratic objectives over nonconvex constraints and solved via the alternating direction method of multipliers…
The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…
We consider multi-task learning, which simultaneously learns related prediction tasks, to improve generalization performance. We factorize a coefficient matrix as the product of two matrices based on a low-rank assumption. These matrices…
The alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco is a benchmark algorithm for two-block separable convex optimization problems with linear equality constraints. It has been modified, specified, and…
We develop and analyze several different second-order algorithms for computing a near-optimal solution path of a convex parametric optimization problem with smooth Hessian. Our algorithms are inspired by a differential equation perspective…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…
This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are…
We study several versions of the alternating direction method of multipliers (ADMM) for solving the convex problem of finding the distance between two ellipsoids and the nonconvex problem of finding the distance between the boundaries of…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…
In this paper, we propose an alternating direction method of multipliers (ADMM)-based optimization algorithm to achieve better undersampling rate for multiple measurement vector (MMV) problem. The core is to introduce the $\ell_{2,0}$-norm…
We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We analyze the convergence rate of the alternating direction method of multipliers (ADMM) for minimizing the sum of two or more nonsmooth convex separable functions subject to linear constraints. Previous analysis of the ADMM typically…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…