Generalized differentials of nonsmooth functions, and necessary conditions for an extremum

DOI10.1007/BF00968624zbMath0583.49016MaRDI QIDQ1069117

Alexander Y. Kruger

Publication date: 1985

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Banach spaceLagrange functionequality and inequality constraintsgeneralized stationarity conditionsnecessary conditions of extremalitynondifferentiable locally Lipschitz functions

Mathematics Subject Classification ID

Nonlinear programming (90C30) Normed linear spaces and Banach spaces; Banach lattices (46B99) Fréchet and Gateaux differentiability in optimization (49J50) Lipschitz (Hölder) classes (26A16) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Derivatives of functions in infinite-dimensional spaces (46G05) Optimality conditions for problems in abstract spaces (49K27) Calculus of functions on infinite-dimensional spaces (26E15)

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Cites Work

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• Generalized gradients of Lipschitz functionals
• On the variational principle
• A general theory of extremals
• Generalized Directional Derivatives and Subgradients of Nonconvex Functions
• Generalized Gradients and Applications
• A New Approach to Lagrange Multipliers
• Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
• Controllability and a Multiplier Rule for Nondifferentiable Optimization Problems

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