Related papers: A Refined Inertial DC Algorithm for DC Programming
The task of approximating an arbitrary convex function arises in several learning problems such as convex regression, learning with a difference of convex (DC) functions, and learning Bregman or $f$-divergences. In this paper, we develop…
The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…
We consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and…
We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We…
The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the…
The goal is to modify the known method of mirror descent (MD), proposed by A.S. Nemirovsky and D.B. Yudin in 1979. The paper shows the idea of a new, so-called inertial MD method with the example of a deterministic optimization problem in…
The objective of this research is to explore a convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem. We introduce four inertial extragradient algorithms that are motivated by the…
We proposed an iterate scheme for solving convex-concave saddle-point problems associated with general convex-concave functions. We demonstrated that when our iterate scheme is applied to a special class of convex-concave functions, which…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
We consider a variable metric and inexact version of the FISTA-type algorithm considered in (Chambolle, Pock, 2016, Calatroni, Chambolle, 2019) for the minimization of the sum of two (possibly strongly) convex functions. The proposed…
In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm…
In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic…
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.…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…
Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…
This paper has two primary objectives. First, we investigate fundamental qualitative properties of the generalized multi-source Weber problem formulated using the Minkowski gauge function. This includes proving the existence of global…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
Deep Actor-Critic algorithms, which combine Actor-Critic with deep neural network (DNN), have been among the most prevalent reinforcement learning algorithms for decision-making problems in simulated environments. However, the existing deep…
Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…