Article
Mathematics
Lu-Chuan Ceng, Li-Jun Zhu, Tzu-Chien Yin
Summary: This article introduces a generalized extragradient implicit method for solving a general system of variational inequalities (GSVI) with the VI and CFPP constraints, and proves the strong convergence of the suggested method under certain assumptions for GSVI problems with the VI and CFPP constraints.
Article
Mathematics, Applied
Xing Wang, Si-Hua Chen, Hai-Yan Qi
Summary: This paper introduces a new class of delay differential variational inequalities and investigates their existence of solutions with boundary conditions. The numerical aspect of the problem is also studied and a numerical scheme is considered, along with a convergence analysis. An application is provided regarding dynamic Nash equilibrium with time delay, specifically focusing on the optimal allocation of distributed generations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Youli Yu, Yeong-Cheng Liou
Summary: This paper studies nonmonotone equilibrium problems and variational inclusion problems in Hilbert spaces. A subgradient algorithm is presented to find a common solution to these problems, and strong convergence of the algorithm is proved.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2022)
Article
Mathematics
Mircea Balaj, Dan Florin Serac
Summary: This paper studies the existence of solutions for generalized equilibrium problems and equilibrium problems. In addition to the given bifunction f, another bifunction is introduced, which are linked by a certain compatibility condition. The uniqueness of the equilibrium theorems in the last section is the absence of the classic equilibrium condition (f(x, x) = 0, for all x in X). The applications given in the paper relate to the Minty variational inequality problem and quasi-equilibrium problems.
Article
Operations Research & Management Science
I. V. Konnov
Summary: In this study, an extension of a non-cooperative game problem involving joint binding constraints is considered. By combining a penalty method and shares allocation of right-hand sides, the initial problem is replaced with a series of usual Nash equilibrium problems and an upper level variational inequality as a master problem. It is shown that under weak coercivity conditions, the solutions of these auxiliary penalized problems converge to a solution of the initial game problem.
Article
Operations Research & Management Science
Lam Quoc Anh, Tran Ngoc Tam, Nguyen Huu Danh
Summary: In this paper, parametric set-valued equilibrium problems in normed spaces are studied. By using the Gerstewitz nonlinear scalarization function and relaxed concavity assumptions, the Lipschitz continuity property of solution maps to such problems is obtained. The treatment and obtained results for these problems are new and different from the existing ones in the literature. The main results are applied to the Browder variational inclusion to illustrate their applicability.
Article
Mathematics, Applied
Lu-Chuan Ceng, Li-Jun Zhu, Tzu-Chien Yin
Summary: This paper introduces a modified algorithm for finding a common solution to a series of problems in a real Hilbert space. The algorithm combines various techniques and approaches, and its strong convergence is proven.
Article
Mathematics, Applied
Simeon Reich, Truong Minh Tuyen, Nguyen Song Ha
Summary: We study variational inequalities over the solution sets of split variational inclusion problems with multiple output sets. In order to find a solution to such problems, we introduce a new parallel iterative algorithm by combining the inertial forward-backward splitting method with the steepest descent method. Some applications of our algorithm to solving split common null point, split minimum point, and split common fixed point problems are also provided.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Construction & Building Technology
Dong Qiao, Guangmin Wang, Meng Xu
Summary: Electric vehicles (EVs) are crucial for reducing air pollution in urban areas as they produce zero emissions. To address the planning problem of fast-charging stations (FCS) for EVs, a two-phase approach consisting of data processing and model optimization is proposed. The developed model aims to minimize the total social cost (TSC) by integrating the maximal coverage location model and charging equilibrium model.
SUSTAINABLE CITIES AND SOCIETY
(2023)
Article
Operations Research & Management Science
L. Q. Anh, P. T. Duoc, T. N. Tam, N. C. Thang
Summary: This paper studies two types of strong set-valued equilibrium problems in Hausdorff locally convex topological vector spaces and establishes stability of solutions in the sense of Hausdorff continuity under suitable assumptions. The main results are then applied to Browder variational inclusions.
OPTIMIZATION LETTERS
(2021)
Article
Mathematics, Applied
Mohammad Dilshad, Doaa Filali, Sumit Chandok, Mohammad Akram
Summary: This paper introduces new iterative methods using the proximal point algorithm to examine a fixed-point problem, equilibrium problem, and a finite collection of variational inclusions in the Hadamard manifold's structure. The paper establishes a strong convergence theorem for the common solution of the stated problems and presents several consequences of the proposed iterative methods and their convergence results.
Article
Mathematics, Applied
Franco Cardin, Cristina Giannotti, Andrea Spiro
Summary: This paper discusses cost minimising control problems with higher order differential constraints and introduces the Principle of Minimal Labour as a condition for optimal solutions. A generalisation of the classical Pontryagin Maximum Principle is derived based on this principle, applicable without the assumption of fixed initial data.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
Wenlong Sun, Yanqiu Liu, Yuanfeng Jin, Choonkil Park
Summary: This paper presents a new iterative algorithm that can find a common element of three types of problems under certain conditions, and proves that the proposed algorithm has strong convergence properties.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2021)
Article
Mathematics, Interdisciplinary Applications
Savin Treanta
Summary: The paper explores the well posedness of a new class of optimization problems involving variational inequality constraints and second-order partial derivatives. By utilizing concepts such as lower semicontinuity, pseudomonotonicity, hemicontinuity, and introducing the set of approximating solutions, the study establishes characterization results on well posedness. Additionally, the theoretical developments are illustrated by presenting examples in the paper.
FRACTAL AND FRACTIONAL
(2021)
Article
Operations Research & Management Science
Lam Quoc Anh
Summary: This paper discusses parametric vector equilibrium problems with equilibrium constraints, introduces the concepts of generalized semicontinuity and convexity of vector-valued maps in ordered spaces, and studies the continuity conditions and sufficient conditions for solution maps.
