On scalar and vector -stable functions

Abstract: The notion of a scalar function that is -stable at a point is introduced in [D. Bednařík, K. Pastor, On second-order conditions in unconstrained optimization, Math. Program. Ser. A 113 (2008) 283–298]. In the present paper a characterization of the -stable functions is obtained. Further, the notion of an -stable function is generalized from scalar to vector functions. In an application, optimality conditions for constrained vector problems with -stable data are established. [ABSTRACT FROM AUTHOR]