Summary: The aim of this paper is to summarize basic facts about $\ell $-stable at a point vector functions and existing results for certain vector constrained programming problem with $\ell$-stable data.
[10] Khanh, P. Q., Tuan, N. D.: Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives. J. Optim. Theory Appl. 133 (2007), 341–357. DOI 10.1007/s10957-007-9169-1 | MR 2333819 | Zbl 1149.90134