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We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
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…
Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…
This paper analyzes the iteration-complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs. More specifically, the objective function is of the form $f + h$…
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proximal operator is available. We establish the exact worst-case…
We consider the problem of minimizing a convex separable objective (as a separable sum of two proper closed convex functions $f$ and $g$) over a linear coupling constraint. We assume that $f$ can be decomposed as the sum of a smooth part…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…