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Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…

We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We show that the…

In this paper, we propose a proximal iteratively reweighted algorithm with extrapolation based on block coordinate update aimed at solving a class of optimization problems which is the sum of a smooth possibly nonconvex loss function and a…

We propose an extension of a special form of gradient descent -- in the literature known as linearised Bregman iteration -- to a larger class of non-convex functions. We replace the classical (squared) two norm metric in the gradient…

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…

In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…

This paper considers distributed optimization for minimizing the average of local nonconvex cost functions, by using local information exchange over undirected communication networks. To reduce the required communication capacity, we…

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…

This paper is devoted to the class of paraconvex functions and presents some of its fundamental properties, characterization, and examples that can be used for their recognition and optimization. Next, the convergence analysis of the…

A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…

We consider minimization of indefinite quadratics with either trust-region (norm) constraints or cubic regularization. Despite the nonconvexity of these problems we prove that, under mild assumptions, gradient descent converges to their…

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

This work considers the non-convex finite sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this…

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…

Decentralized minimax optimization has been actively studied in the past few years due to its application in a wide range of machine learning models. However, the current theoretical understanding of its convergence rate is far from…

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

We consider convex and nonconvex constrained optimization with a partially separable objective function: agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables…