Related papers: Zero-Convex Functions, Perturbation Resilience, an…

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…

In this paper, we study the convergence of an interior subgradient and proximal methods for a DC (difference of convex functions) constrained minimization problem.

Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…

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…

This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical…

In this paper, we investigate a class of constrained saddle point (SP) problems where the objective function is nonconvex-concave and smooth. This class of problems has wide applicability in machine learning, including robust multi-class…

In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…

A framework is presented whereby a general convex conic optimization problem is transformed into an equivalent convex optimization problem whose only constraints are linear equations and whose objective function is Lipschitz continuous.…

Predict and optimize is an increasingly popular decision-making paradigm that employs machine learning to predict unknown parameters of optimization problems. Instead of minimizing the prediction error of the parameters, it trains…

Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

Conditional gradient methods have attracted much attention in both machine learning and optimization communities recently. These simple methods can guarantee the generation of sparse solutions. In addition, without the computation of full…

We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…

We study a method that involves principally convex feasibility-seeking and makes secondary efforts of objective function value reduction. This is the well-known superiorization method (SM), where the iterates of an asymptotically convergent…

This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…

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…

We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…

In this paper, we consider the problem of learning high-dimensional tensor regression problems with low-rank structure. One of the core challenges associated with learning high-dimensional models is computation since the underlying…