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On the Existence and the Stability of Solutions in Nonconvex Vector Optimization $$^\dagger $$ †

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  • Tran Van Nghi

    (Hanoi Pedagogical University 2)

  • Le Ngoc Kien

    (Hanoi Pedagogical University 2
    Vietnam-Hungary Industrial University)

  • Nguyen Van Tuyen

    (Hanoi Pedagogical University 2)

Abstract

The paper is devoted to the existence of weak Pareto solutions and the weak sharp minima at infinity property for a general class of constrained nonconvex vector optimization problems with unbounded constraint set via asymptotic cones and generalized asymptotic functions. Then we show that these conditions are useful for studying the solution stability of nonconvex vector optimization problems with linear perturbation. We also provide some applications for a subclass of robustly quasiconvex vector optimization problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02831-0
    DOI: 10.1007/s10957-025-02831-0
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    References listed on IDEAS

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    1. Jonathan M. Borwein, 1983. "On the Existence of Pareto Efficient Points," Mathematics of Operations Research, INFORMS, vol. 8(1), pages 64-73, February.
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    7. 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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