On scalar and vector ℓ -stable functions

The notion of a scalar function that is ℓ -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 ℓ -stable functions is obtained. Further, the not...

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Veröffentlicht in:	Nonlinear analysis 2011, Vol.74 (1), p.182-194
1. Verfasser:	Ginchev, Ivan
Format:	Artikel
Sprache:	eng
Schlagworte:	[formula omitted] functions [formula omitted]-stable functions Calculus of variations and optimal control Exact sciences and technology Lipschitz functions Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Optimality conditions Sciences and techniques of general use Vector optimization
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Zusammenfassung:	The notion of a scalar function that is ℓ -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 ℓ -stable functions is obtained. Further, the notion of an ℓ -stable function is generalized from scalar to vector functions. In an application, optimality conditions for constrained vector problems with ℓ -stable data are established.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2010.08.032