Iterative Methods for Random Generalized Quasi Variational Inequalities With Applications

WANG Yannan; ZENG Jiaqin; HUANG Nanjing

doi:10.21656/1000-0887.440199

Volume 44 Issue 11

Nov. 2023

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WANG Yannan, ZENG Jiaqin, HUANG Nanjing. Iterative Methods for Random Generalized Quasi Variational Inequalities With Applications[J]. Applied Mathematics and Mechanics, 2023, 44(11): 1378-1388. doi: 10.21656/1000-0887.440199

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Iterative Methods for Random Generalized Quasi Variational Inequalities With Applications

doi: 10.21656/1000-0887.440199

School of Mathematics, Sichuan University, Chengdu 610064, P.R.China

Received Date: 2023-06-29
Rev Recd Date: 2023-07-21
Publish Date: 2023-11-01

Abstract

Abstract

To obtain the iterative methods for solving a class of random generalized quasi variational inequalities (RGQVIs) in the Hilbert spaces, the measurability of the projection operators on varying-constraint sets depicted by the mapping from points to random-value sets with closed (convex) values, was proved. Moreover, the random iterative algorithm was proposed for solving RGQVIs, and the convergence of the random sequences generated with the random iterative algorithm was obtained under some suitable conditions of monotony and Lipschitz continuity. Finally, 2 applications were given with depicting results of the random generalized Nash games and random Walrasian equilibrium problems, respectively.
- random quasi variational inequality,
- random iterative algorithm,
- convergence,
- random Nash equilibrium,
- random Walrasian equilibrium

(Contributed by HUANG Nanjing, M. AMM Ediorial Board)

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References(32)

References

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