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Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis

Author

Listed:
  • Felipe Lara

    (Universidad de Tarapacá)

  • Nguyen Van Tuyen

    (Hanoi Pedagogical University 2)

  • Tran Van Nghi

    (Hanoi Pedagogical University 2)

Abstract

We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.

Suggested Citation

  • Felipe Lara & Nguyen Van Tuyen & Tran Van Nghi, 2025. "Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis," Journal of Global Optimization, Springer, vol. 92(4), pages 933-950, August.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:4:d:10.1007_s10898-025-01516-2
    DOI: 10.1007/s10898-025-01516-2
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    References listed on IDEAS

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    1. 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.
    2. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, December.
    3. 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.
    4. Felipe Lara & Rubén López, 2017. "Formulas for Asymptotic Functions via Conjugates, Directional Derivatives and Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 793-811, June.
    5. 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.
    6. Alfred Auslender, 1996. "Noncoercive Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 769-782, November.
    7. 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.
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    Cited by:

    1. Tran Van Nghi & Le Ngoc Kien & Nguyen Van Tuyen, 2026. "On the Existence and the Stability of Solutions in Nonconvex Vector Optimization $$^\dagger $$ †," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-26, January.

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