# Bing TanUniversity of Electronic Science and Technology of China | UESTC · Institute of Fundamental and Frontier Sciences

Bing Tan

Ph.D. Candidate

Operator Theory and Applications

## About

61

Publications

7,744

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

285

Citations

Citations since 2016

Introduction

Bing Tan, as an international visiting Ph.D. student, is now at The University of British Columbia, Okanagan, under the supervision of Prof. Shawn Wang, with research interests in operator theory and applications.
My personal homepage: https://bingtan.me.

**Skills and Expertise**

## Publications

Publications (61)

In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algor...

In this paper, two new projection-type algorithms are introduced for solving pseudomonotone variational inequalities in real Hilbert spaces. The proposed methods use two non-monotonic step sizes allowing them to work adaptively without the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the proposed meth...

The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterio...

The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known....

In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong con...

We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work ad...

In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experimen...

We provide two novel projection and contraction algorithms to find the minimum-norm solution of the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in a real Hilbert space. Our algorithms can work adaptively without requiring the prior information of the Lipschitz constant of the operator. Strong convergen...

This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each i...

To handle pseudomonotone variational inequality problems in real Hilbert spaces, four modified inertial projection and contraction algorithms with non-monotonic step sizes are suggested in this paper. The proposed algorithms take advantage of a novel non-monotonic step size criteria, allowing them to work without previous knowledge of the Lipschitz...

In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant o...

In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong...

The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible...

This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorit...

In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping....

In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the opera...

In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can...

This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step si...

In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operato...

We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to...

An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical e...

In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adapt...

In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and q-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.

In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under s...

In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowl...

This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can...

In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical expe...

In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence...

The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some...

This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self‐adaptive step‐size sequence, which does...

In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally,...

In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are est...

In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems...

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where t...

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 the suggested algorithms are proved without the prior knowle...

The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup J={S_{λ}: λ \in Q} of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related resul...

We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Str...

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergenc...

In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion...

The paper introduces two inertial Mann algorithms to find solutions of hierarchical fixed point problems of nonexpansive mappings. We obtain strong convergence theorems in Hilbert spaces under suitable conditions. Some numerical examples are provided to illustrate the numerical behavior of the algorithms and numerical results show that our proposed...

The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong convergence theorems are obtained under mild conditions. Finally, some numerical experiments demonstrate the effici...

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed under the effect of self-adaptive stepsizes which does not require information of the norms of the given oper...

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...

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on mappings. Finally, some numerical examples are presented t...

In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for nonexpansive mappings in Hilbert spaces and get s...

In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms...

In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The re...

We investigate an inertial viscosity-type Tseng's extragradient algorithm with a new step size to solve pseudomonotone variational inequality problems in real Hilbert spaces. A strong convergence theorem of the algorithm is obtained without the prior information of the Lipschitz constant of the operator and also without any requirement of additiona...

The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms only need to calculate the projection on the feasible set once in each it...

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 inertial method, the subgradient extragradient method, the Tseng's extragradient method and the Mann-type meth...

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...

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where th...

In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonexpansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, whic...

In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorith...

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on mappings. Finally, some numerical examples are presented t...

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...

We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The alg...

In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm....

In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms an...

In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem,...

In this paper, we introduce two new modified inertial Mann Halpern and viscosity algorithms for solving fixed point problems. We establish strong convergence theorems under some suitable conditions. Finally, our algorithms are applied to split feasibility problem, convex feasibility problem and location theory. The algorithms and results presented...