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Solving Mixed Variational Inequalities Via a Proximal Neurodynamic Network with Applications

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Abstract

This paper proposes a proximal neurodynamic network (PNDN) for solving mixed variational inequalities based on the proximal operator. It is shown that the proposed PNDN is globally exponentially stable under some mild conditions, and a stop** condition is provided for the PNDN. Furthermore, the proposed PNDN is applied in solving variational inequalities and composition optimization with nonsmooth regularization. In addition, the equilibrium point of the proposed proximal gradient neurodynamic network for composition optimization problems is globally exponentially stable via the Polyak-Lojasiewicz condition, a relaxation of strong convexity. Finally, numerical and experimental examples on sparse signal reconstruction and variational arc-flow problems are presented to validate the effectiveness of the proposed neurodynamic network.

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Acknowledgements

This work was supported by the National Key Research and Development Project under Grant 2018AAA0100101, the National Natural Science Foundation of China under Grant 62003281, the Fundamental Research Funds for the Central Universities under Grant XDJK2020TY003 and Grant SWU020006, and the National Natural Science Foundation of China under 61873213 and Grant 61633011, the Graduate Student Innovation Project of Chongqing under Grant CYB21126 .

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Authors and Affiliations

  1. Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, School of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    **ngxing Ju, Hangjun Che, Chuandong Li & **ng He

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  1. **ngxing Ju
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  2. Hangjun Che
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  3. Chuandong Li
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  4. **ng He
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Correspondence to Hangjun Che.

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Ju, X., Che, H., Li, C. et al. Solving Mixed Variational Inequalities Via a Proximal Neurodynamic Network with Applications. Neural Process Lett 54, 207–226 (2022). https://doi.org/10.1007/s11063-021-10628-1

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