The Implicit Function Theorem

By Steven G. Krantz, Harold R. Parks. 2002

372 citations recorded by the source corpus.

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In Theoretical Computer Science

Citations in the corpus

DisCor: Corrective Feedback in Reinforcement Learning via Distribution Correction (2020, methodology): “The IFT gradient is given by: ∂Qk ∂pk ∣∣∣∣∣ Qk,pk = − [Diag(pk)]−1 [Diag(Qk − B∗Qk−1)] .”
THE IMPLICIT AND THE INVERSE FUNCTION THEOREMS: EASY PROOFS (2012, background): “nverse Function Theorem) and further developments (as in diﬀerentiable manifolds, Riemannian geometry, partial diﬀerential equations, numerical analysis, etc.) we refer the reader to Krantz and Parks [14], Dontchev and Rockafellar [7, pp. 7–8, 57–59], Hurwicz and Richter [11], Iurato [12], and Scarp”
A global Implicit Function Theorem without initial point and its applications to control of non-affine systems of high dimensions (2006, background): “Those requirements motivated many generalizations of the Implicit Function Theorem in various spaces and manifolds [1,4,5,17,20]. The book [ 18 ] by S.G.”
A Game Theoretic Framework for Model Based Reinforcement Learning (2020, neutral): “…to approximate the best response, while the leader learns slowly. dLA (θA,θ∗B(θA)) dθA = dθ∗B dθA ∂LA(θA,θB) ∂θB ∣∣∣∣ θB=θ∗B + ∂LA(θA,θB) ∂θA ∣∣∣∣ θB=θ∗B (11) The implicit Jacobian term (dθ∗B/dθA) can be obtained using the implicit function theorem (Krantz & Parks, 2002; Rajeswaran et al., 2019).”
Connected Substitutes and Invertibility of Demand (2011, background): “…use the latter implication to establish nonparametric identi ability of rms marginal costs and to testability of alternative models 15See e.g., Palais (1959), Ho (1975), Parthasarathy (1983), Parthasarathy and Ravindran (2003), and Krantz and Parks (2002) for various statements of this result.”
A tutorial on multiobjective optimization: fundamentals and evolutionary methods (2018, background): “See for the implicit function theorem, for instance, Krantz and Parks (2003).”
A Change-of-Variable Formula with Local Time on Curves (2005, neutral): “[3] p.”