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

Tran Van Nghi (), Le Ngoc Kien () and Nguyen Van Tuyen ()
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Tran Van Nghi: Hanoi Pedagogical University 2
Le Ngoc Kien: Hanoi Pedagogical University 2
Nguyen Van Tuyen: Hanoi Pedagogical University 2

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 2, 26 pages

Abstract: 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.

Keywords: Vector optimization; Existence; Stability; Weak sharp minima; Asymptotic cone; Asymptotic function; Linear perturbation; 90C29; 49J30; 90C31; 90C26; 49J52 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02831-0

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