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Solving Mixed Variational Inequalities Beyond Convexity

Author

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  • Sorin-Mihai Grad

    (University of Vienna)

  • Felipe Lara

    (Universidad de Tarapacá)

Abstract

We show that Malitsky’s recent Golden Ratio Algorithm for solving convex mixed variational inequalities can be employed in a certain nonconvex framework as well, making it probably the first iterative method in the literature for solving generalized convex mixed variational inequalities, and illustrate this result by numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:2:d:10.1007_s10957-021-01860-9
    DOI: 10.1007/s10957-021-01860-9
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    9. Papa Quiroz, E.A. & Mallma Ramirez, L. & Oliveira, P.R., 2015. "An inexact proximal method for quasiconvex minimization," European Journal of Operational Research, Elsevier, vol. 246(3), pages 721-729.
    10. Alfredo Iusem & Felipe Lara, 2019. "Optimality Conditions for Vector Equilibrium Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 187-206, January.
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    Cited by:

    1. Alfredo Iusem & Felipe Lara & Raúl T. Marcavillaca & Le Hai Yen, 2024. "A Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming," Journal of Global Optimization, Springer, vol. 90(3), pages 755-779, November.
    2. 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.
    3. Deng, Huaijun & Liu, Linna & Fang, Jianyin & Qu, Boyang & Huang, Quanzhen, 2023. "A novel improved whale optimization algorithm for optimization problems with multi-strategy and hybrid algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 794-817.
    4. A. Iusem & F. Lara, 2022. "Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 443-461, June.
    5. S.-M. Grad & F. Lara & R. T. Marcavillaca, 2023. "Relaxed-inertial proximal point type algorithms for quasiconvex minimization," Journal of Global Optimization, Springer, vol. 85(3), pages 615-635, March.
    6. Pham Ngoc Anh & Qamrul Hasan Ansari & Ho Phi Tu, 2023. "DC auxiliary principle methods for solving lexicographic equilibrium problems," Journal of Global Optimization, Springer, vol. 85(1), pages 129-153, January.

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