Second-order subdifferentials of \(C^{1,1}\) functions and optimality conditions

DOI10.1007/BF00425960zbMath0864.49012OpenAlexW1985892316MaRDI QIDQ1915624

Nadia P. Zlateva, Pando Grigorov Georgiev

Publication date: 14 January 1997

Published in: Set-Valued Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00425960

zbMATH Keywords

necessary and sufficient optimality conditionsdirectional derivativesecond-order subdifferentialsGâteaux derivativestwice strict differentiability

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Fréchet and Gateaux differentiability in optimization (49J50) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (21)

Generalization of \(C^{1,1}\) property in infinite dimension ⋮ Second-order optimality conditions for constrained optimization problems with \(C^1\) data via regular and limiting subdifferentials ⋮ On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming ⋮ Necessary conditions for vector optimization in infinite dimension ⋮ Parametric method for global optimization ⋮ Second-order optimality conditions for inequality constrained problems with locally Lipschitz data ⋮ On scalar and vector \(\ell \)-stable functions ⋮ On relations of vector optimization results with \(C^{1,1}\) data ⋮ First and second-order optimality conditions for nonsmooth vector optimization using set-valued directional derivatives ⋮ Second-order conditions for constrained vector optimization problems with ℓ-stable data ⋮ Second-order optimality conditions for problems with \(C^{1}\) data ⋮ Differentiability properties of functions that are \(\ell \)-stable at a point ⋮ Differentiability properties of \(\ell\)-stable vector functions in infinite-dimensional normed spaces ⋮ Parametric proximal-point methods ⋮ On second-order conditions in unconstrained optimization ⋮ Stability in generalized differentiability based on a set convergence principle ⋮ Sufficient Conditions of Isolated Minimizers for Constrained Programming Problems ⋮ On necessary optimality conditions for nonsmooth vector optimization problems with mixed constraints in infinite dimensions ⋮ Fréchet approach in second-order optimization ⋮ A note on second-order optimality conditions ⋮ Second-order conditions in \(C^{1,1}\) constrained vector optimization

Cites Work

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• Generalized Second Derivatives of Convex Functions and Saddle Functions
• Characterizations of the plenary hull of the generalized Jacobian matrix
• Optimization and nonsmooth analysis
• First- and Second-Order Epi-Differentiability in Nonlinear Programming
• On generalized differentials and subdifferentials of Lipschitz vector-valued functions
• Second-order conditions in c^{1, 1}optimization with applications
• Second-order moderate derivatives
• Set-valued analysis

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