A new Tseng method for supply chain network equilibrium model

Zhuang Shan; Leyou Zhang; Zhuang Shan; Leyou Zhang

doi:10.3934/mbe.2023338

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 7828-7844. doi: 10.3934/mbe.2023338

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Theory article Special Issues

A new Tseng method for supply chain network equilibrium model

Zhuang Shan ,
Leyou Zhang ^,

School of Mathematics and Statistics, Xidian University, Xi'an 710126, China

Academic Editor: Regino Criado Herrero

Received: 30 December 2022 Revised: 02 February 2023 Accepted: 07 February 2023 Published: 21 February 2023

To solve the equilibrium problem of the supply chain network, a new subgradient extragradient method is introduced. The proposal achieves adaptive parameter selection, and supports a one-step subgradient projection operator, which can theoretically reduce the computational complexity of the algorithm. The introduction of subgradient projection operators makes the calculation of algorithms easier, and transforms the projection difficulty problem into how to find suitable sub-differential function problems. The given convergence proof further shows the advantages of the proposed algorithm. Finally, the presented algorithm is operated to a concrete supply chain network model. The comparisons show the proposed algorithm is better than other methods in term of CPU running time and iteration steps.
Citation: Zhuang Shan, Leyou Zhang. A new Tseng method for supply chain network equilibrium model[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 7828-7844. doi: 10.3934/mbe.2023338

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Abstract

To solve the equilibrium problem of the supply chain network, a new subgradient extragradient method is introduced. The proposal achieves adaptive parameter selection, and supports a one-step subgradient projection operator, which can theoretically reduce the computational complexity of the algorithm. The introduction of subgradient projection operators makes the calculation of algorithms easier, and transforms the projection difficulty problem into how to find suitable sub-differential function problems. The given convergence proof further shows the advantages of the proposed algorithm. Finally, the presented algorithm is operated to a concrete supply chain network model. The comparisons show the proposed algorithm is better than other methods in term of CPU running time and iteration steps.

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