scholarly journals Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach

2019 ◽  
Vol 15 (4) ◽  
pp. 1653-1675 ◽  
Author(s):  
Liping Pang ◽  
◽  
Fanyun Meng ◽  
Jinhe Wang ◽  
Keyword(s):  
Variational Inequality ◽  
Inequality Constraint ◽  
Stationary Points ◽  
Asymptotic Convergence ◽  
Multiobjective Programs ◽  
Parametric Variational Inequality

scholarly journals Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 187
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
General System ◽  
Inequality Constraint ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution ◽  
Common Fixed Point Problem ◽  
Monotone Variational Inequality

In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Strong convergence of the proposed method to the unique solution of the problem is established under some suitable assumptions.

scholarly journals Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 218
Author(s):  
Lu-Chuan Ceng ◽  
Xiaoye Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mappings ◽  
General System ◽  
Inequality Constraint ◽  
Common Solution ◽  
Iteration Methods ◽  
Monotone Variational Inequality ◽  
Implicit Iteration

This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions.

scholarly journals Convergence theorems for composite viscosity approaches to systems variational inequalities in Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6267-6281
Author(s):  
Lu-Chuan Ceng ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Infinite Family ◽  
General System ◽  
Inequality Constraint ◽  
Implicit And Explicit

In this paper, we study a general system of variational inequalities with a hierarchical variational inequality constraint for an infinite family of nonexpansive mappings. We introduce general implicit and explicit iterative algorithms. We prove the strong convergence of the sequences generated by the proposed iterative algorithms to a solution of the studied problems.

scholarly journals Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Meiju Luo ◽  
Kun Zhang
Keyword(s):  
Variational Inequality ◽  
Objective Function ◽  
Vector Variational Inequality ◽  
Low Risk ◽  
Variational Inequality Problems ◽  
Stationary Points ◽  
Conditional Value At Risk ◽  
Convergence Results ◽  
Approximation Problems ◽  
Stochastic Vector

In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk conditional value-at-risk (CVaR) model. However, this low-risk CVaR model is difficult to solve by the general constraint optimization algorithm. This is because the objective function is nonsmoothing function, and the objective function contains expectation, which is not easy to be computed. By using the sample average approximation technique and smoothing function, we present the corresponding approximation problems of the low-risk CVaR model to deal with these two difficulties related to the low-risk CVaR model. In addition, for the given approximation problems, we prove the convergence results of global optimal solutions and the convergence results of stationary points, respectively. Finally, a numerical experiment is given.

scholarly journals Hybrid Mann Viscosity Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 142 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
General System ◽  
Inequality Constraint ◽  
Common Fixed Points ◽  
Common Solution ◽  
Implicit Iteration

In the present work, we introduce a hybrid Mann viscosity-like implicit iteration to find solutions of a monotone classical variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities and a problem of common fixed points of an asymptotically nonexpansive mapping and a countable of uniformly Lipschitzian pseudocontractive mappings in Hilbert spaces, which is called the triple hierarchical constrained variational inequality. Strong convergence of the proposed method to the unique solution of the problem is guaranteed under some suitable assumptions. As a sub-result, we provide an algorithm to solve problem of common fixed points of pseudocontractive, nonexpansive mappings, variational inequality problems and generalized mixed bifunction equilibrium problems in Hilbert spaces.

scholarly journals Solving a Class of Equilibrium Problems With Equilibrium Constraints*

2021 ◽  
Author(s):  
Peiyu Li ◽  
Ke-Wei Ding
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Stationary Points ◽  
Generalized Nash Equilibrium Problem ◽  
Generalized Nash Equilibrium ◽  
Equilibrium Constraints ◽  
Nash Equilibrium Problem ◽  
Mathematical Programs ◽  
Shared Constraints ◽  
Parametric Variational Inequality

Abstract An equilibrium problem with equilibrium constraints (EPEC) can be looked on as a generalized Nash equilibrium problem (GNEP) and the mathematical programs with equilibrium constraints (MPEC) whose constraints contain a parametric variational inequality or complementarity system. In this paper, we particularly consider a class of EPEC and solve its normalized stationary points where the multipliers of the leaders on the shared constraints are proportionable. We reformulate this kind of EPEC to a standard MPEC. In addition, we demonstrate the proposed approach on an EPEC model in similar products market.

scholarly journals A Class of Nonlinear Fuzzy Variational Inequality Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 54
Author(s):  
Cunlin Li ◽  
Zhifu Jia ◽  
Yeong-Cheng Liou
Keyword(s):  
Variational Inequality ◽  
Historical Data ◽  
Variational Inequality Problems ◽  
Stationary Points ◽  
Optimal Solutions ◽  
Approximation Model ◽  
Fuzzy Variables ◽  
Global Optimal ◽  
Residual Minimization ◽  
Nonlinear Variational Inequality

In this paper, we consider nonlinear variational inequality problems with fuzzy variables. The fuzzy variables were introduced to deal with the variational inequality containing noise for which historical data is not available. The fuzzy expected residual minimization (FERM) problems were established. We discussed the S C 1 property of the FERM model. Furthermore, results of convergence analysis were obtained based on an approximation model of the FERM model. The convergence of global optimal solutions and the convergence of stationary points were analysed.

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