Related papers: Golden Ratio Algorithms for Variational Inequaliti…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
We prove the first convergence guarantees for a subgradient method minimizing a generic Lipschitz function over generic Lipschitz inequality constraints. No smoothness or convexity (or weak convexity) assumptions are made. Instead, we…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
In our pursuit of finding a zero for a monotone and Lipschitz continuous operator $M : \R^n \rightarrow \R^n$ amidst noisy evaluations, we explore an associated differential equation within a stochastic framework, incorporating a correction…
This paper considers the nonconvex nonsmooth problem in which the objective function is Lipschitz continuous. We focus on the stochastic setting where the algorithm can access stochastic function value evaluations with heavy-tailed noise,…
In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration.…
The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…
In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…
This paper considers the problem for finding the $(\delta,\epsilon)$-Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of important applications. We construct a zeroth-order…
In this paper, we propose an inexact golden ratio primal-dual algorithm with linesearch step(IP-GRPDAL) for solving the saddle point problems, where two subproblems can be approximately solved by applying the notations of inexact extended…
In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in…
This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…
Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…
Let $E = L_p, \; 1<p\leq 2,$ and $A : E \to E^*$ be a bounded monotone map such that $0 \in R(A)$. In this paper, we introduce and study an algorithm for approximating zeros of $A$. Furthermore, we study the application of this algorithm to…
This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…
Newton's method has been an important approach for solving variational inequalities, quasi-Newton method is a good alternative choice to save computational cost. In this paper, we propose a new method for solving monotone variational…
The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost…