A Chain Rule for Essentially Smooth Lipschitz Functions

DOI10.1137/S1052623496297838zbMath0923.49011MaRDI QIDQ4389193

Moors, Warren B., Jonathan M. Borwein

Publication date: 12 May 1998

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

zbMATH Keywords

chain ruleLipschitz functionClarke generalized derivativearcwise essentially smooth functions

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20)

Related Items (10)

Links between functions and subdifferentials ⋮ Essentially smooth Lipschitz functions ⋮ Path differentiability of ODE flows ⋮ Conservative parametric optimality and the ridge method for tame min-max problems ⋮ Upper semismooth functions and the subdifferential determination property ⋮ Generalized Jacobian for functions with infinite dimensional range and domain ⋮ Directional upper derivatives and the chain rule formula for locally Lipschitz functions on Banach spaces ⋮ Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning ⋮ Examples of Pathological Dynamics of the Subgradient Method for Lipschitz Path-Differentiable Functions ⋮ Nonsmooth bundle trust-region algorithm with applications to robust stability

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