scholarly journals Probabilistic feasibility guarantees for solution sets to uncertain variational inequalities

Automatica ◽  
2022 ◽  
Vol 137 ◽  
pp. 110120
Author(s):  
Filippo Fabiani ◽  
Kostas Margellos ◽  
Paul J. Goulart
Keyword(s):  
Variational Inequalities ◽  
Solution Sets

scholarly journals Connectedness of Solution Sets for Weak Vector Variational Inequalities on Unbounded Closed Convex Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Ren-you Zhong ◽  
Yun-liang Wang ◽  
Jiang-hua Fan
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Convex Sets ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Solution Set ◽  
Solution Sets ◽  
Finite Dimensional ◽  
Path Connectedness ◽  
Weak Vector

We study the connectedness of solution set for set-valued weak vector variational inequality in unbounded closed convex subsets of finite dimensional spaces, when the mapping involved is scalarC-pseudomonotone. Moreover, the path connectedness of solution set for set-valued weak vector variational inequality is established, when the mapping involved is strictly scalarC-pseudomonotone. The results presented in this paper generalize some known results by Cheng (2001), Lee et al. (1998), and Lee and Bu (2005).

On variational inequalities and nonlinear programming problem

2008 ◽  
Vol 45 (4) ◽  
pp. 483-491
Author(s):  
Vsevolod Ivanov
Keyword(s):  
Variational Inequality ◽  
Nonlinear Programming ◽  
Variational Inequalities ◽  
Programming Problem ◽  
Directional Derivative ◽  
Nonlinear Programming Problem ◽  
Solution Sets ◽  
Minty Variational Inequality ◽  
Stampacchia Variational Inequality ◽  
Dini Directional Derivative

In this paper the Stampacchia variational inequality, the Minty variational inequality, and the respective nonlinear programming problem are investigated in terms of the lower Dini directional derivative. We answer the questions which are the largest classes of functions such that the solution sets of each pair of these problems coincide.

scholarly journals On a class of generalized stochastic Browder mixed variational inequalities

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Chao Min ◽  
Fei-fei Fan ◽  
Zhao-zhong Yang ◽  
Xiao-gang Li
Keyword(s):  
Variational Inequalities ◽  
Existence Of Solutions ◽  
Uniqueness Of Solution ◽  
Measurable Selection ◽  
Stochastic Variational Inequalities ◽  
Selection Theorem ◽  
Solution Sets ◽  
Mixed Variational Inequalities

AbstractIn this paper, we introduce a class of stochastic variational inequalities generated from the Browder variational inequalities. First, the existence of solutions for these generalized stochastic Browder mixed variational inequalities (GS-BMVI) are investigated based on FKKM theorem and Aummann’s measurable selection theorem. Then the uniqueness of solution for GS-BMVI is proved based on strengthening conditions of monotonicity and convexity, the compactness and convexity of the solution sets are discussed by Minty’s technique. The results of this paper can provide a foundation for further research of a class of stochastic evolutionary problems driven by GS-BMVI.

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