## On scalar and vector $$\ell$$-stable functions.(English)Zbl 1205.26007

Summary: The notion of a scalar function that is $$\ell$$-stable at a point is introduced in [D. Bednařík and K. Pastor, Math. Program. Ser. A 113, No. 2 (A), 283–298 (2008; Zbl 1211.90276)]. In the present paper a characterization of the $$\ell$$-stable functions is obtained. Further, the notion of an $$\ell$$-stable function is generalized from scalar to vector functions. In an application, optimality conditions for constrained vector problems with $$\ell$$-stable data are established.

### MSC:

 26A16 Lipschitz (Hölder) classes 90C29 Multi-objective and goal programming 90C46 Optimality conditions and duality in mathematical programming 49J52 Nonsmooth analysis

Zbl 1211.90276
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### References:

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