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A general asymptotic function with applications in nonconvex optimization

Author

Listed:
  • Nicolas Hadjisavvas

    (University of the Aegean)

  • Felipe Lara

    (Universidad de Tarapacá)

  • Dinh The Luc

    (Ton Duc Thang University
    Ton Duc Thang University)

Abstract

We introduce a new concept of asymptotic functions which allows us to simultaneously study convex and concave functions as well as quasiconvex and quasiconcave functions. We provide some calculus rules and most relevant properties of the new asymptotic functions for application purpose. We also compare them with the classical asymptotic functions of convex analysis. By using the new concept of asymptotic functions we establish sufficient conditions for the nonemptiness and for the boundedness of the solution set of quasiconvex minimization problems and quasiconcave maximization problems. Applications are given for quadratic and fractional quadratic problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:1:d:10.1007_s10898-020-00891-2
    DOI: 10.1007/s10898-020-00891-2
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    References listed on IDEAS

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    1. Dinh The Luc & Michel Théra, 1994. "Derivatives with Support and Applications," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 659-675, August.
    2. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, October.
    3. 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.
    4. Nicolas Hadjisavvas & Felipe Lara & Juan Enrique Martínez-Legaz, 2019. "A Quasiconvex Asymptotic Function with Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 170-186, January.
    5. 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.
    6. Fabián Flores-Bazán & Fernando Flores-Bazán & Cristián Vera, 2015. "Maximizing and minimizing quasiconvex functions: related properties, existence and optimality conditions via radial epiderivatives," Journal of Global Optimization, Springer, vol. 63(1), pages 99-123, September.
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