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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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    1. Giancarlo Bigi & Mauro Passacantando, 2017. "Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 63-79, November.
    2. Alfredo Iusem & Felipe Lara, 2020. "A Note on “Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces”," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 607-608, November.
    3. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, October.
    4. M.A. Noor, 2002. "Proximal Methods for Mixed Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 447-452, November.
    5. Muhammad Aslam Noor & Zhenyu Huang, 2012. "Some Proximal Methods for Solving Mixed Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, May.
    6. D. Goeleven, 2008. "Existence and Uniqueness for a Linear Mixed Variational Inequality Arising in Electrical Circuits with Transistors," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 397-406, September.
    7. Nils Langenberg & Rainer Tichatschke, 2012. "Interior proximal methods for quasiconvex optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 641-661, March.
    8. 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.
    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.
    11. Corbet, Shaen & Goodell, John W. & Günay, Samet, 2020. "Co-movements and spillovers of oil and renewable firms under extreme conditions: New evidence from negative WTI prices during COVID-19," Energy Economics, Elsevier, vol. 92(C).
    12. Fu-Quan Xia & Nan-Jing Huang, 2011. "A Projection-Proximal Point Algorithm for Solving Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 98-117, July.
    13. 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.
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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