相关论文: Approximation analysis for the minimization proble…

In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…

We show that the primal-dual gradient method, also known as the gradient descent ascent method, for solving convex-concave minimax problems can be viewed as an inexact gradient method applied to the primal problem. The gradient, whose exact…

We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…

We study approximations to the Moreau envelope -- and infimal convolutions more broadly -- based on Laplace's method, a classical tool in analysis which ties certain integrals to suprema of their integrands. We believe the connection…

This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate…

This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…

This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the…

Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc)…

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…

The purpose of the paper is to give a complete characterization of the continuity of lower envelopes in the infinite dimensional spaces in terms of the notion of c-regularity. As an application we introduce a variational unconstrained…

We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…

Optimization problems with uncertainty in the constraints occur in many applications. Particularly, probability functions present a natural form to deal with this situation. Nevertheless, in some cases, the resulting probability functions…

The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…

Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…

Given an orthogonal lattice with mesh length h on a bounded convex domain, we propose to approximate the Aleksandrov solution of the Monge-Ampere equation by regularizing the data and discretizing the equation in a subdomain using the…

The article considers the discrete analogue of the method of quickest descent for an inverse Acoustics problem in case of a smooth source. The authors derived the gradient of functional in differential and discrete cases, described the…

This paper presents a multilevel FISTA algorithm, based on the use of the Moreau envelope to build the correction brought by the coarse models, which is easy to compute when the explicit form of the proximal operator of the considered…

There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…