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Solving Constrained Pseudoconvex Optimization Problems with deep learning-based neurodynamic optimization

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  • Wu, Dawen
  • Lisser, Abdel

Abstract

In this paper, we consider Constrained Pseudoconvex Nonsmooth Optimization Problems (CPNOPs), which are a class of nonconvex optimization problems. Due to their nonconvexity, classical convex optimization algorithms are unable to solve them, while existing methods, i.e., numerical integration methods, are inadequate in terms of computational performance. In this paper, we propose a novel approach for solving CPNOPs that combines neurodynamic optimization with deep learning. We construct an initial value problem (IVP) involving a system of ordinary differential equations for a CPNOP and use a surrogate model based on a neural network to approximate the IVP. Our approach transforms the CPNOP into a neural network training problem, leveraging the power of deep learning infrastructure to improve computational performance and eliminate the need for traditional optimization solvers. Our experimental results show that our approach is superior to numerical integration methods in terms of both solution quality and computational efficiency.

Suggested Citation

  • Wu, Dawen & Lisser, Abdel, 2024. "Solving Constrained Pseudoconvex Optimization Problems with deep learning-based neurodynamic optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 424-434.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:424-434
    DOI: 10.1016/j.matcom.2023.12.032
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    References listed on IDEAS

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    1. Bo Jiang & Tianyi Lin & Shiqian Ma & Shuzhong Zhang, 2019. "Structured nonconvex and nonsmooth optimization: algorithms and iteration complexity analysis," Computational Optimization and Applications, Springer, vol. 72(1), pages 115-157, January.
    2. Liao, Guangyuan & Zhang, Limin, 2022. "Solving flows of dynamical systems by deep neural networks and a novel deep learning algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 331-342.
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