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.

In many engineering problems, we face multi-objective optimization, with several objective functions f₁,...,fₙ. We want to provide the user with the Pareto set-a set of all possible solutions x which cannot be improved in all categories (i.e., for which $f_j\left(x^{\text{'}}\right)\ge f_j\left(x\right)$ for all j and $f_j\left(x\right)>f_j\left(x\right)$ for some j is impossible). The user should be able to select an appropriate trade-off between, say, cost and durability. We extend the general results about (verified) algorithmic computability of maxima locations to show that Pareto...