In this paper we propose a splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions. At each iteration of the algorithm, two strongly convex subprograms are required to solve separately, one for each component bifunction. In contrast to the splitting algorithms previously proposed in Anh and Hai (Numer. Algorithms 76 (2017) 67–91) and Hai and Vinh (Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 111 (2017) 1051–1069), our algorithm is convergent for paramonotone and strongly pseudomonotone bifunctions without any Lipschitz type as well as Hölder continuity condition of the bifunctions involved. Furthermore, we show that the ergodic sequence defined by the algorithm iterates converges to a solution without paramonotonicity property. Some numerical experiments on differentiated Cournot-Nash models are presented to show the behavior of our proposed algorithm with and without ergodic.
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DOI : 10.1051/ro/2020030
Keywords: Monotone equilibria, splitting algorithm, ergodic sequence
@article{RO_2021__55_S1_S1395_0,
author = {Duc, Phung Minh and Le, Xuan Thanh},
title = {A splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions and application to cournot-nash model},
journal = {RAIRO. Operations Research},
pages = {S1395--S1410},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020030},
mrnumber = {4223121},
zbl = {1472.90139},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020030/}
}
TY - JOUR AU - Duc, Phung Minh AU - Le, Xuan Thanh TI - A splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions and application to cournot-nash model JO - RAIRO. Operations Research PY - 2021 SP - S1395 EP - S1410 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020030/ DO - 10.1051/ro/2020030 LA - en ID - RO_2021__55_S1_S1395_0 ER -
%0 Journal Article %A Duc, Phung Minh %A Le, Xuan Thanh %T A splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions and application to cournot-nash model %J RAIRO. Operations Research %D 2021 %P S1395-S1410 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020030/ %R 10.1051/ro/2020030 %G en %F RO_2021__55_S1_S1395_0
Duc, Phung Minh; Le, Xuan Thanh. A splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions and application to cournot-nash model. RAIRO. Operations Research, Tome 55 (2021), pp. S1395-S1410. doi: 10.1051/ro/2020030
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