Article
Multidisciplinary Sciences
Kanikar Muangchoo, Nasser Aedh Alreshidi, Ioannis K. Argyros
Summary: This paper introduces two novel extragradient-like methods to solve variational inequalities in real Hilbert spaces. The designed methods use a specific step size rule and demonstrate strong convergence. Numerical experiments are provided to showcase the superior performance of the methods.
Article
Mathematics
Chainarong Khunpanuk, Bancha Panyanak, Nuttapol Pakkaranang
Summary: Two new inertial-type extragradient methods are proposed for solving the variational inequality problem and the fixed point problem. These methods use self-adaptive step size rules and have strong convergence properties under appropriate conditions. Numerical examples demonstrate the effectiveness and validation of the proposed methods.
Article
Mathematics, Applied
Fei Ma, Jun Yang, Min Yin
Summary: An algorithm for solving variational inequalities problems with Lipschitz continuous and pseudomonotone mapping in Banach space is introduced in this paper. By modifying the subgradient extragradient method with a new and simple iterative step size, the strong convergence to a common solution of the variational inequalities and fixed point problems is established without the knowledge of the Lipschitz constant. Finally, a numerical experiment is conducted to support the results.
Article
Operations Research & Management Science
Thong Duong Viet, Luong Van Long, Xiao-Huan Li, Qiao-Li Dong, Yeol Je Cho, Pham Anh Tuan
Summary: This paper introduces a new algorithm based on the subgradient extragradient method for solving a pseudomonotone variational inequality problem with the Lipschitz condition in real Hilbert spaces. The algorithm demonstrates weak convergence under pseudomonotonicity and Lipschitz continuity, with a nonasymptotic O(1/n) convergence rate, and strong convergence under strong pseudomonotonicity and Lipschitz continuity assumptions. Numerical results are provided to demonstrate the computational effectiveness of the algorithm.
Article
Mathematics, Applied
Duong Viet Thong, Qiao-Li Dong, Lu-Lu Liu, Nguyen Anh Triet, Nguyen Phuong Lan
Summary: In this work, two new iterative schemes are proposed for finding a solution to a pseudo-monotone, Lipschitz continuous variational inequality problem in real Hilbert spaces. The algorithms have the advantage of not requiring prior knowledge and only compute one projection onto a feasible set per iteration, without using sequentially weak continuity. An R-linear convergence rate is obtained under additional assumptions. Numerical examples are provided to illustrate the effectiveness of the algorithms.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
L. O. Jolaoso, X. Qin, Y. Shehu, J-C Yao
Summary: In this paper, improved subgradient extragradient algorithms are proposed to solve pseudo-monotone variational inequalities in real Hilbert spaces, including cases with and without Lipschitz condition, and their convergence and convergence rate are proven under mild conditions. The numerical behavior of the proposed algorithms is also studied and compared with known methods in the literature.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2021)
Article
Mathematics, Applied
Zai-Yun Peng, Dan Li, Yong Zhao, Ren-Li Liang
Summary: This paper proposes an accelerated subgradient extragradient algorithm with a new non-monotonic step size to solve bilevel variational inequality problems involving non-Lipschitz continuous operator in Hilbert spaces. The algorithm only requires one projection onto the feasible set during each iteration and does not require prior knowledge of the Lipschitz constant. Under suitable and weaker conditions, the algorithm achieves strong convergence. Numerical tests demonstrate the efficiency and advantages of the proposed algorithm.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Zai-Yun Peng, Zhi-Ying Peng, Gang Cai, Gao-Xi Li
Summary: In this paper, an inertial subgradient extragradient algorithm is proposed to solve the pseudomonotone variational inequality problems in Banach space. The new line-search rule is employed in this iterative scheme. The strong convergence theorems for the proposed algorithms are established under the assumptions that the operators are non-Lipschitz continuous. Furthermore, several numerical experiments are given to demonstrate that the proposed method has better convergence performance than the existing ones in the literature.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics, Applied
Habib Ur Rehman, Poom Kumam, Wiyada Kumam, Kamonrat Sombut
Summary: This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for rho$$ \rho $$-demicontractive mapping in real Hilbert spaces. The algorithms utilize self-adaptive variable step size rules and do not require prior knowledge of the operator value. The study obtained two strong convergence theorems without previous knowledge of the operator's Lipschitz constant. Numerical experiments were conducted to evaluate the efficacy and applicability of the algorithms, supporting and extending previous findings on variational inequality and fixed point problems.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Nopparat Wairojjana, Nuttapol Pakkaranang, Nattawut Pholasa
Summary: In this paper, a new algorithm for solving pseudomonotone variational inequalities in a real Hilbert space with Lipschitz-type condition is introduced. The algorithm employs a step size rule based on local operator information and operates without knowledge of the Lipschitz constant of an operator, demonstrating strong convergence. Numerical results are provided to evaluate the computational performance of the algorithm.
DEMONSTRATIO MATHEMATICA
(2021)
Article
Mathematics, Applied
Huanqin Wu, Zhongbing Xie, Min Li
Summary: In this paper, the classical subgradient extragradient method is combined with the Bregman projection method to solve variational inequality problems in reflexive Banach spaces. Two different parameters are set in the two-step projections, unlike consistent parameters in other results. The application of the inertial technique accelerates the iteration efficiency. Finally, the proposed algorithm is compared with other known results and it is found that our method effectively improves the convergence process.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Computer Science, Software Engineering
Xiaokai Chang, Sanyang Liu, Zhao Deng, Suoping Li
Summary: This paper introduces an efficient subgradient extragradient method for solving variational inequality problems with a monotone operator in Hilbert space. An inertial subgradient extragradient algorithm with adaptive step sizes is proposed to overcome the limitations of existing methods, avoiding the need for two values of the operator and Lipschitz constant. Numerical experiments demonstrate the efficiency of the algorithm.
OPTIMIZATION METHODS & SOFTWARE
(2022)
Article
Mathematics, Applied
Zhongbing Xie, Gang Cai, Xiaoxiao Li, Qiao-Li Dong
Summary: This paper introduces a new algorithm for solving variational inequality problems involving pseudomonotone and uniformly continuous operator in Banach spaces. A strong convergence theorem is proved by constructing a new line-search rule. Several numerical experimental results are also provided to demonstrate the performance of the proposed algorithm.
ANALYSIS AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Zhongbing Xie, Gang Cai, Xiaoxiao Li, Qiao-Li Dong
Summary: In this paper, a new method is introduced to solve variational inequalities involving pseudomonotone and Lipschitz operators. The convergence rate of the algorithm is accelerated by using a new step size rule, and numerical examples are presented to support the main results.
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Jun Yang
Summary: This paper introduces an inertial algorithm for solving classical variational inequalities in real Hilbert space with Lipschitz continuous and pseudomonotone mapping. The algorithm, inspired by subgradient extragradient method and inertial method, utilizes a new step size. Convergence is established without knowledge of the Lipschitz constant of the mapping, and numerical experiments demonstrate the efficiency and advantage of the proposed algorithm.
APPLICABLE ANALYSIS
(2021)
