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A neural network approach to solve geometric programs with joint probabilistic constraints

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  • Tassouli, Siham
  • Lisser, Abdel

Abstract

We study a dynamical neural network approach to solve nonconvex geometric programs with joint probabilistic constraints (GPPC for short) with normally distributed coefficients and independent matrix row vectors. The main feature of our framework is to solve the biconvex deterministic equivalent problem of GPPC without the use of any convex approximation unlike the state-of-the-art solving methods. The second feature of our approach is to solve the dynamical system without the use of any iterative method but only by solving an ordinary differential equation system. We prove the stability together with the convergence of our neural network in the sense of Lyapunov. We also prove the equivalence between the optimal solution of the deterministic equivalent problem of GPPC and the solution of the dynamical system. We provide numerical experiments to show the performances of our approach compared to the state-of-art.

Suggested Citation

  • Tassouli, Siham & Lisser, Abdel, 2023. "A neural network approach to solve geometric programs with joint probabilistic constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 765-777.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:765-777
    DOI: 10.1016/j.matcom.2022.10.025
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    References listed on IDEAS

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    1. Jochen Gorski & Frank Pfeuffer & Kathrin Klamroth, 2007. "Biconvex sets and optimization with biconvex functions: a survey and extensions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 373-407, December.
    2. Rashed Khanjani-Shiraz & Salman Khodayifar & Panos M. Pardalos, 2021. "Copula theory approach to stochastic geometric programming," Journal of Global Optimization, Springer, vol. 81(2), pages 435-468, October.
    3. Gongxian Xu & Lei Wang, 2014. "An Improved Geometric Programming Approach for Optimization of Biochemical Systems," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, June.
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