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Ginchev, Ivan

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

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 1, 182-194 (2011).
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.

Cited in 5 Documents

MSC:

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

Keywords:

\(\ell \)-stable functions; Lipschitz functions; \(C^{1,1}\) functions; vector optimization; optimality conditions

Citations:

Zbl 1211.90276
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\textit{I. Ginchev}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 1, 182--194 (2011; Zbl 1205.26007)
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References:

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