Inverse and implicit function theorems forH-differentiable and semismooth functions
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We extend the classical inverse and implicit function theorems, the implicit function theorems of Lyusternik and Graves, and the results of Clarke and Pourciau to the situation when the given function is not smooth, but it has a convex strict prederivative whose measure of noncom
Implicit-function theorems for generalized equations play an important role in many applications, especially in the stability and sensitivity analysis of variational inequalities and optimization problems and in the convergence analysis of numerical algorithms solving such proble
Adjoint Algorithmic Differentiation is an efficient way to obtain financial instrument price derivatives with respect to the data inputs. Often the differentiation does not cover the full pricing process when a model calibration is performed. Thanks to the implicit function theor
In this paper we elaborate new methods to the theory of parametric generalized equations governed by accretive mappings. Two implicit function theorems will be proved, one for m-accretive and another for locally accretive and continuous set-valued mappings. Making use of the theo
There is the work by Bridges et al (1999) on the key features of a constructive proof of the implicit function theorem, including some applications to physics and mechanics. For mixtures of logistic distributions such information is lacking, although a special instance of the imp
The implicit function theorem is a statement of the existence, continuity, and differentiability of a function or set of functions. The theorem is closely related to the convergence of Newton’s method for nonlinear equations, the existence and uniqueness of solutions to nonlinear