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Self-Adaptive Inertial Projection and Contraction Algorithm for Monotone Variational Inequality

Author

Listed:
  • Xue Gao

    (School of Mathematical Sciences, Jiangsu Key Lab for NSLSCS, Nanjing Normal University, Nanjing 210023, P. R. China)

  • Xingju Cai

    (School of Mathematical Sciences, Jiangsu Key Lab for NSLSCS, Nanjing Normal University, Nanjing 210023, P. R. China)

  • Xueye Wang

    (Qishuyan Senior High School of Changzhou, Changzhou 213011, P. R. China)

Abstract

In this paper, we propose a self-adaptive inertial projection and contraction algorithm, by combining backtracking search with the inertial projection and contraction algorithm, for solving monotone variational inequality in Hilbert space. This algorithm not only circumvents the restrictive assumption of Lipschitz continuity of the operator, but also gives more suitable and feasible parameters. Under the assumption that the operator is continuous and monotone, we establish weak convergence for proposed algorithm. Finally, we report some preliminary computational results to show the efficiency and advantage of the algorithm.

Suggested Citation

  • Xue Gao & Xingju Cai & Xueye Wang, 2022. "Self-Adaptive Inertial Projection and Contraction Algorithm for Monotone Variational Inequality," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(02), pages 1-21, April.
    • Handle: RePEc:wsi:apjorx:v:39:y:2022:i:02:n:s0217595921500214
    DOI: 10.1142/S0217595921500214
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