Decrease of \(C^{1,1}\) property in vector optimization. (English) Zbl 1193.49016

Bednařík, Dušan; Pastor, Karel

RAIRO, Oper. Res. 43, No. 4, 359-372 (2009).

Summary: We generalize sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Rocca, and by authors with the help of the notion of \(\ell\)-stability for vector functions.

MSC:

49K10	Optimality conditions for free problems in two or more independent variables
49J52	Nonsmooth analysis
49J50	Fréchet and Gateaux differentiability in optimization
90C29	Multi-objective and goal programming
90C30	Nonlinear programming
49K40	Sensitivity, stability, well-posedness

Keywords:

\(C^{1, 1}\) function; \(\ell\)-stable function; generalized second-order directional derivative; Dini derivative; weakly efficient minimizer; isolated minimizer of second-order