An inertial Tseng's extragradient method for solving multi-valued variational inequalities with one projection

双层变分不等式问题的Bregman惯性迭代正则化外梯度方法

A Bregman inertial iteratively regularized extragradient method for bilevel variational inequality problems

本文提出一种Bregman惯性正则化外梯度方法求解双层变分不等式问题，在偶空间进行惯性外推，推导了广义间隙函数的非渐近收敛界，并通过交通网络和多投资组合纳什均衡实验验证了有效性。

Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng's F-B four-operator splitting method for solving monotone inclusions

In this paper, we propose and study the iteration complexity of an inexact Douglas-Rachford splitting (DRS) method and a Douglas-Rachford-Tseng's forward-backward (F-B) splitting method for solving two-operator and four-operator monotone inclusions, respectively. The former method (although based on a slightly different mechanism of iteration) is motivated by the recent work of J. Eckstein and W. Yao, in which an inexact DRS method is derived from a special instance of the hybrid proximal extragradient (HPE) method of Solodov and Svaiter, while the latter one combines the proposed inexact DRS …

Self adaptive inertial extragradient algorithms for solving variational inequality problems

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 real Hilbert spaces. Strong convergence theorems for our algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performances of the proposed algorithms and provide a comparison with related ones.

非凸优化问题的一种含惯性项的Tseng型近似算法

An inertial Tseng's type proximal algorithm for nonsmooth and nonconvex optimization problems

本文研究了在非凸情况下，通过非光滑函数与光滑函数之和的最小化问题，提出了一种具有惯性和记忆效应的前向-后向-前向近似算法，并证明了其收敛性。

一种带有惯性效应的混合近端-反梯度算法

A hybrid proximal-extragradient algorithm with inertial effects

本文提出一种结合惯性项的混合近端-反梯度算法，研究其在实希尔伯特空间中求解极大单调算子零点的收敛性，结合扩展Fejér单调性技术与Opial引理分析，并展示经典算法可嵌入该框架。

求解变分不等式与不动点问题的惯性外梯度算法的强收敛性

Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems

本文提出两种惯性外梯度算法，用于求解单调Lipschitz变分不等式与半压缩不动点问题的公共解，无需Lipschitz常数先验信息和线搜索，每次迭代仅需一次投影，并证明了强收敛性。

用于单调包含的强收敛惯性非精确邻近点算法及其在变分不等式中的应用

A strongly convergent inertial inexact proximal-point algorithm for monotone inclusions with applications to variational inequalities

本文提出一种在更弱惯性参数假设下强收敛的惯性非精确邻近点算法，并给出迭代复杂度分析，将其应用于变分不等式，得到多种经典方法的强收敛惯性变体，数值实验验证了其有效性。

一种改进的双惯性子梯度extragradient算法用于非单调变分不等式及其应用

A modified double inertial subgradient extragradient algorithm for non-monotone variational inequality with applications

本文提出了一种改进的双惯性迭代方法，用于解决非单调变分不等式问题，通过自适应步长规则在不预先知道算子Lipschitz常数的情况下实现弱收敛，并讨论了不同算子类型的收敛性及线性收敛性。

The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces

Tseng's forward-backward-forward algorithm is a valuable alternative for Korpelevich's extragradient method when solving variational inequalities over a convex and closed set governed by monotone and Lipschitz continuous operators, as it requires in every step only one projection operation. However, it is well-known that Korpelevich's method converges and can therefore be used also for solving variational inequalities governed by pseudo-monotone and Lipschitz continuous operators. In this paper, we first associate to a pseudo-monotone variational inequality a forward-backward-forward dynamical…

外梯度型方法及其在余次单调包含问题上的 $\mathcal{O}(1/k)$ 末次迭代收敛速率

Extragradient-Type Methods with $\mathcal{O} (1/k)$ Last-Iterate Convergence Rates for Co-Hypomonotone Inclusions

本文提出两种Nesterov加速的外梯度方法求解余次单调包含问题，分别基于Tseng分裂和“过去”FBFS方案，在适当条件下证明残差范数达到$\mathcal{O}(1/k)$末次迭代收敛速率，并给出额外锚定梯度方法的对比分析。

非 Lipschitz 连续算子变分不等式的自适应投影方法收敛性分析

Convergence Analysis of the Self-Adaptive Projection Method for Variational Inequalities with Non-Lipschitz Continuous Operators

针对非 Lipschitz 连续拟单调算子的变分不等式，提出带自适应步长的 Tseng 超梯度方法，证明温和条件下的收敛性，并通过数值实验验证其有效性与优越性。

Forward-backward-forward methods with variance reduction for stochastic variational inequalities

We develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities. Our method builds on Tseng's forward-backward-forward (FBF) algorithm, which is known in the deterministic literature to be a valuable alternative to Korpelevich's extragradient method when solving variational inequalities over a convex and closed set governed by pseudo-monotone, Lipschitz continuous operators. The main computational advantage of Tseng's algorithm is that it relies only on a single projection step and two independent queries of a stochastic oracle. Our…

一种带有新步长规则的两步惯性方法用于Hilbert空间中的变分不等式

A two-step inertial method with a new step-size rule for variational inequalities in hilbert spaces

本文提出了一种新的两步惯性方法，用于求解Hilbert空间中的变分不等式，该方法结合自适应和Armijo型步长规则，无需Lipschitz条件，具有更广的应用范围。

A Relaxed Inertial Forward-Backward-Forward Algorithm for Solving Monotone Inclusions with Application to GANs

We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. This work aims to extend Tseng's forward-backward-forward method by both using inertial effects as well as relaxation parameters. We formulate first a second order dynamical system which approaches the solution set of the monotone inclusion problem to be solved and provide an asymptotic analysis for its trajectories. We provide for RIFBF, which follows by explicit time di…

用新惯性技术求解均衡问题

Solving Equilibrium Problem with New Inertial Technique

本文提出一种结合惯性与修正项的次梯度extragradient方法，用于高效求解均衡问题，并在特定条件下实现线性收敛。

Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems

In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.