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An Inertial-type CG Projection Method with Restart for Pseudo-monotone Costs with Application to Traffic Assignment

Author

Listed:
  • Pengjie Liu

    (China University of Mining and Technology)

  • Linhao Li

    (China University of Mining and Technology)

  • Hu Shao

    (China University of Mining and Technology)

  • Meixing Liu

    (Yulin Normal University)

  • Jiaxu Fan

    (China University of Mining and Technology)

Abstract

In practical computational applications, many models can be transformed into systems of nonlinear equations for resolution. In this paper, we introduce an inertial-type conjugate gradient projection method that incorporates a restart procedure to solve it. Within the restart procedure, we suggest a new two-term composite restart direction with a flexible non-zero vector and also introduce a tuning parameter, the spectral parameter, as part of the restart direction. Moreover, we design a new self-adaptive line search, which is well-defined. The suggested search direction, which integrates the restart procedure, possesses the sufficient descent and trust region properties, eliminating the need for additional conditions. To achieve the theoretical convergence for the introduced method, we discuss a specific scenario involving pseudo-monotone costs, namely, the system of nonlinear pseudo-monotone equations, without requiring the Lipschitz continuity and monotonicity assumptions. To evaluate the effectiveness of the introduced method, we conduct comparative tests against existing methods on nonlinear equations. Finally, the practicality of the introduced method is demonstrated through its application to the traffic assignment problem.

Suggested Citation

  • Pengjie Liu & Linhao Li & Hu Shao & Meixing Liu & Jiaxu Fan, 2025. "An Inertial-type CG Projection Method with Restart for Pseudo-monotone Costs with Application to Traffic Assignment," Networks and Spatial Economics, Springer, vol. 25(1), pages 147-172, March.
    • Handle: RePEc:kap:netspa:v:25:y:2025:i:1:d:10.1007_s11067-024-09653-z
    DOI: 10.1007/s11067-024-09653-z
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    References listed on IDEAS

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    1. Pingjing Xia & Gang Cai & Qiao-Li Dong, 2023. "A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(4), pages 931-952, December.
    2. Chinedu Izuchukwu & Yekini Shehu, 2021. "New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems Beyond Monotonicity," Networks and Spatial Economics, Springer, vol. 21(2), pages 291-323, June.
    3. Chuanwei Wang & Yiju Wang & Chuanliang Xu, 2007. "A projection method for a system of nonlinear monotone equations with convex constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 33-46, August.
    4. Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2024. "Strong Convergent Inertial Two-subgradient Extragradient Method for Finding Minimum-norm Solutions of Variational Inequality Problems," Networks and Spatial Economics, Springer, vol. 24(2), pages 425-459, June.
    5. Chinedu Izuchukwu & Grace N. Ogwo & Yekini Shehu, 2024. "Proximal Point Algorithms with Inertial Extrapolation for Quasi-convex Pseudo-monotone Equilibrium Problems," Networks and Spatial Economics, Springer, vol. 24(3), pages 681-706, September.
    6. Jianghua Yin & Jinbao Jian & Guodong Ma, 2024. "A modified inexact Levenberg–Marquardt method with the descent property for solving nonlinear equations," Computational Optimization and Applications, Springer, vol. 87(1), pages 289-322, January.
    7. Duong Viet Thong & Phan Tu Vuong & Pham Ky Anh & Le Dung Muu, 2022. "A New Projection-type Method with Nondecreasing Adaptive Step-sizes for Pseudo-monotone Variational Inequalities," Networks and Spatial Economics, Springer, vol. 22(4), pages 803-829, December.
    8. Xiaoyu Wu & Hu Shao & Pengjie Liu & Yue Zhuo, 2023. "An Inertial Spectral CG Projection Method Based on the Memoryless BFGS Update," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1130-1155, September.
    9. Duong Viet Thong & Pham Ky Anh & Vu Tien Dung & Do Thi My Linh, 2023. "A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities," Networks and Spatial Economics, Springer, vol. 23(1), pages 39-64, March.
    10. Yekini Shehu & Lulu Liu & Qiao-Li Dong & Jen-Chih Yao, 2022. "A Relaxed Forward-Backward-Forward Algorithm with Alternated Inertial Step: Weak and Linear Convergence," Networks and Spatial Economics, Springer, vol. 22(4), pages 959-990, December.
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