On Fréchet Subdifferentials

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Toward Off-Policy Learning Control with Function Approximation (2010, unknown): “(1) Due to the chain-rule of subdifferentials (e.g., Kruger, 2003), it follows that ifˆϕ t+1 (θ) is an unbiased estimate of the subgradient of V t+1 (θ) (given S t+1 ), then b t+1 (θ) = γ ˆ ϕ t+1 (θ) − ϕ t is a subdifferential to δ t+1 (θ) and thus E[ b t+1 (θ)ϕ t ] E ϕ t ϕ t −1 E[ δ t+1 (θ)ϕ t ] =…”
Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming (2006, unknown): “Some versions of this result, as well as related calculus rules for Fréchet subgradients, were formulated by Kruger [4].”
A Globally Convergent Algorithm for Nonconvex Optimization Based on Block Coordinate Update (2014, unknown): “2 (Limiting Fréchet subdifferential [26]).”
Apprenticeship Learning using Inverse Reinforcement Learning and Gradient Methods (2007, background): “Kruger (2003)).”
Error Bounds: Necessary and Sufficient Conditions (2010, methodology): “We start with recalling the well known notion of the Fréchet subdifferential of f at x̄ (see for instance [34,38]):”
ABOUT STATIONARITY AND REGULARITY IN VARIATIONAL ANALYSIS (2009, background): “The last 639 inclusion is equivalent (see [29,39]) to x∗ ∈ ∂f(x̄).”