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Volume 11 Issue 7
Jul.  2024

IEEE/CAA Journal of Automatica Sinica

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Article Contents
W. He and  Y. Wang,  “Distributed optimal variational GNE seeking in merely monotone games,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 7, pp. 1621–1630, Jul. 2024. doi: 10.1109/JAS.2024.124284
Citation: W. He and  Y. Wang,  “Distributed optimal variational GNE seeking in merely monotone games,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 7, pp. 1621–1630, Jul. 2024. doi: 10.1109/JAS.2024.124284

Distributed Optimal Variational GNE Seeking in Merely Monotone Games

doi: 10.1109/JAS.2024.124284
Funds:  This work was supported by the National Natural Science Foundation of China (Basic Science Center Program) (61988101), the Joint Fund of Ministry of Education for Equipment Pre-research (8091B022234), Shanghai International Science and Technology Cooperation Program (21550712400), Shanghai Pilot Program for Basic Research (22TQ1400100-3), the Fundamental Research Funds for the Central Universities, and Shanghai Artifcial Intelligence Laboratory
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  • In this paper, the optimal variational generalized Nash equilibrium (v-GNE) seeking problem in merely monotone games with linearly coupled cost functions is investigated, in which the feasible strategy domain of each agent is coupled through an affine constraint. A distributed algorithm based on the hybrid steepest descent method is first proposed to seek the optimal v-GNE. Then, an accelerated algorithm with relaxation is proposed and analyzed, which has the potential to further improve the convergence speed to the optimal v-GNE. Some sufficient conditions in both algorithms are obtained to ensure the global convergence towards the optimal v-GNE. To illustrate the performance of the algorithms, numerical simulation is conducted based on a networked Nash-Cournot game with bounded market capacities.


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    • An algorithm is proposed to seek the optimal GNE in a distributed manner
    • Each agent adjusts its update step size solely based on its local information
    • An algorithm, augmented with relaxation acceleration scheme, is also proposed to expedite the convergence speed
    • when the optimal relaxation parameter is difficult to obtain. The time-varying relaxation parameter is adopted to achieve a trade-off in acceleration effects


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