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.

scholarly journals Weighted Method for Uncertain Nonlinear Variational Inequality Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 974
Author(s):  
Cunlin Li ◽  
Mihai Postolache ◽  
Zhifu Jia
Keyword(s):  
Variational Inequality ◽  
Approximation Method ◽  
Uncertain Variable ◽  
Variational Inequality Problems ◽  
Event Space ◽  
Residual Function ◽  
Compact Approximation ◽  
Global Optimal ◽  
Residual Minimization ◽  
Nonlinear Variational Inequality

A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the convergence of the global optimal solutions of the uncertain weighted expected residual minimization model is given through the integration by parts method under the compact space of the uncertain event. The limiting behaviors of the transformed model are analyzed. Furthermore, a compact approximation method is proposed in the unbounded uncertain event space. Through analysis of the convergence of UWERM model and reasonable hypothesis, the compact approximation method is verified under the circumstance of Holder continuity.

scholarly journals Generalized nonlinear variational inequality problems involving multivalued mappings

1997 ◽  
Vol 10 (3) ◽  
pp. 289-295 ◽  
Author(s):  
Ram U. Verma
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problems ◽  
Multivalued Mappings ◽  
Strongly Monotone ◽  
Nonlinear Variational Inequality

The solvability of a class of generalized nonlinear variational inequality problems involving multivalued, strongly monotone and strongly Lipschitz (a special type) operators, which are closely associated with generalized nonlinear complementarily problems, is discussed.

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.

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