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A neural dynamic system for solving convex nonlinear optimization problems with hybrid constraints

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Abstract

This paper proposes a neural network model for solving convex nonlinear optimization problems (CNOP) with equality and inequality constraints, whose equilibrium point coincides with the solution of Karush–Kuhn–Tucker points of the CNOP. Based on equality transformation and a Fischer–Burmeister function, we first transform the CNOP into a unconstrained minimization problem via a merit function. Then, using the steepest descent method, the neural network is constructed. On the basis of the convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, the proposed network is proved to be stable in the sense of Lyapunov and converges to the optimal solution of the CNOP. Moreover, the proposed neural network is proved to be exponentially stable. Comparing with the existing models, the proposed neural network has fewer variables and neurons, which makes circuit realization easier. Simulation results show the feasibility and efficiency of the proposed network.

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Acknowledgements

The authors would like to thank the Editor, Associate Editor and the reviewers for their insightful and constructive comments, which help to enrich the contents and improve the presentation of the results in this paper. This work is partially supported by National Natural Science Foundation of China (No. 61473136) and the Fundamental Research Funds for the Central Universities (No. JUSRP51322B).

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Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, 214122, China

    Xinjian Huang

  2. The School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China

    Baotong Cui

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  1. Xinjian Huang
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  2. Baotong Cui
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Correspondence to Xinjian Huang.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. There is no professional or other personal interest of any nature or kind in any product, service and company that could be construed as influencing the position presented in the manuscript entitled “A neural dynamic system for solving convex nonlinear optimization problems with hybrid constraints.”

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Huang, X., Cui, B. A neural dynamic system for solving convex nonlinear optimization problems with hybrid constraints. Neural Comput & Applic 31, 6027–6038 (2019). https://doi.org/10.1007/s00521-018-3422-4

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  • DOI: https://doi.org/10.1007/s00521-018-3422-4

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