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A Variational Inequality Based Stochastic Approximation for Inverse Problems in Stochastic Partial Differential Equations

In: Nonlinear Analysis and Global Optimization

Author

Listed:
  • Rachel Hawks

    (Rochester Institute of Technology)

  • Baasansuren Jadamba

    (Rochester Institute of Technology)

  • Akhtar A. Khan

    (Rochester Institute of Technology)

  • Miguel Sama

    (Universidad Nacional de Educación a Distancia)

  • Yidan Yang

    (Rochester Institute of Technology)

Abstract

The primary objective of this work is to study the inverse problem of identifying a parameter in partial differential equations with random data. We explore the nonlinear inverse problem in a variational inequality framework. We propose a projected-gradient-type stochastic approximation scheme for general variational inequalities and give a complete convergence analysis under weaker conditions on the random noise than those commonly imposed in the available literature. The proposed iterative scheme is tested on the inverse problem of parameter identification. We provide a derivative characterization of the solution map, which is used in computing the derivative of the objective map. By employing a finite element based discretization scheme, we derive the discrete formulas necessary to test the developed stochastic approximation scheme. Preliminary numerical results show the efficacy of the developed framework.

Suggested Citation

  • Rachel Hawks & Baasansuren Jadamba & Akhtar A. Khan & Miguel Sama & Yidan Yang, 2021. "A Variational Inequality Based Stochastic Approximation for Inverse Problems in Stochastic Partial Differential Equations," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Nonlinear Analysis and Global Optimization, pages 207-226, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-61732-5_9
    DOI: 10.1007/978-3-030-61732-5_9
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    Cited by:

    1. Annamaria Barbagallo & Serena Guarino Lo Bianco, 2023. "A random time-dependent noncooperative equilibrium problem," Computational Optimization and Applications, Springer, vol. 84(1), pages 27-52, January.

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    Keywords

    35R30; 49N45; 65J20; 65J22; 65M30;
    All these keywords.

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