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Complementarity and Variational Inequalities in Electronics

In: Operations Research, Engineering, and Cyber Security

Author

Listed:
  • Khalid Addi

    (University of La Reunion, PIMENT)

  • Daniel Goeleven

    (University of La Reunion, PIMENT)

Abstract

The purpose of this chapter is to review and describe the main mathematical models applicable to the study of electrical networks involving devices like diodes whose Ampere–Volt characteristics are set-valued graphs. The mathematical models in question are related to complementarity problems, variational inequalities, and non-regular dynamical systems.

Suggested Citation

  • Khalid Addi & Daniel Goeleven, 2017. "Complementarity and Variational Inequalities in Electronics," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Operations Research, Engineering, and Cyber Security, pages 1-43, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-51500-7_1
    DOI: 10.1007/978-3-319-51500-7_1
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    Citations

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    Cited by:

    1. Samir Adly, 2019. "A Coderivative Approach to the Robust Stability of Composite Parametric Variational Systems: Applications in Nonsmooth Mechanics," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 62-90, January.
    2. Nicolas Hadjisavvas & Felipe Lara & Dinh The Luc, 2020. "A general asymptotic function with applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 78(1), pages 49-68, September.
    3. Shih-Sen Chang & Salahuddin & Lin Wang & Jinfang Tang & Liangcai Zhao, 2022. "Optimal Control Problems for Set-Valued Quasivariational Inequalities with Applications," Mathematics, MDPI, vol. 10(5), pages 1-19, February.
    4. L. F. Bueno & G. Haeser & F. Lara & F. N. Rojas, 2020. "An Augmented Lagrangian method for quasi-equilibrium problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 737-766, July.
    5. Samir Adly & Tahar Haddad & Ba Khiet Le, 2019. "State-Dependent Implicit Sweeping Process in the Framework of Quasistatic Evolution Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 473-493, August.
    6. Sorin-Mihai Grad & Felipe Lara, 2021. "Solving Mixed Variational Inequalities Beyond Convexity," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 565-580, August.
    7. Felipe Lara & Rubén López & Benar F. Svaiter, 2019. "A Further Study on Asymptotic Functions via Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 366-382, July.
    8. Tong-tong Shang & Guo-ji Tang, 2023. "Mixed polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 86(4), pages 953-988, August.
    9. Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.
    10. Chinedu Izuchukwu & Yekini Shehu & Chibueze C. Okeke, 2023. "Extension of forward-reflected-backward method to non-convex mixed variational inequalities," Journal of Global Optimization, Springer, vol. 86(1), pages 123-140, May.
    11. Alfredo Iusem & Felipe Lara, 2019. "Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 122-138, October.

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