\(\ell \)-stable functions are continuous

DOI10.1016/j.na.2008.03.011zbMath1158.49022OpenAlexW2057913012MaRDI QIDQ1004629

Karel Pastor, Dušan Bednařík

Publication date: 11 March 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.03.011

zbMATH Keywords

locally Lipschitz functionregular functionDini derivative\(C^{1,1}\) functionPeano derivativestable functionisolated minimizer of order \(k\)

Mathematics Subject Classification ID

Continuity and differentiation questions (26B05) Optimality conditions for free problems in two or more independent variables (49K10)

Related Items (10)

Generalization of \(C^{1,1}\) property in infinite dimension ⋮ Necessary conditions for vector optimization in infinite dimension ⋮ On \(\ell \)-stable mappings with values in infinite-dimensional Banach spaces ⋮ On scalar and vector \(\ell \)-stable functions ⋮ On second-order optimality conditions in constrained multiobjective optimization ⋮ Second-order optimality conditions with the envelope-like effect in nonsmooth multiobjective mathematical programming. I: \(l\)-stability and set-valued directional derivatives ⋮ Second-order conditions for constrained vector optimization problems with ℓ-stable data ⋮ Relation between the class of M. Sama and the class of \(\ell\)-stable functions ⋮ Sufficient Conditions of Isolated Minimizers for Constrained Programming Problems ⋮ Fréchet approach in second-order optimization

Cites Work

• Unnamed Item
• Technical note: Directional derivatives in nonsmooth optimization
• From scalar to vector optimization.
• On second-order conditions in unconstrained optimization
• A Generalized Second-Order Derivative in Nonsmooth Optimization
• Stability in Mathematical Programming with Nondifferentiable Data
• Elimination of Strict Convergence in Optimization

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