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Higher derivative tensors from univariate Taylor series with comparison to Maple on an engineering problem
ReviewAbstract: We consider the problem of evaluating partial derivatives of a vector function defined by a computerPalabras claves:Autores:Andreas Griewank, Vogel O., Walther A.Fuentes:scopusFinite convergence of an active signature method to local minima of piecewise linear functions
ArticleAbstract: We previously derived first-order (KKT) and second-order (SOSC) optimality conditions for functionsPalabras claves:abs-normal form, active set and signature, Karush–Kuhn–Tucker (KKT), linear independence kink qualification (LIKQ), normal growth, quadratic regularization, Successive abs-linear minimization (SALMIN), tangential stationarityAutores:Andreas Griewank, Walther A.Fuentes:scopusFirst- and second-order optimality conditions for piecewise smooth objective functions
ArticleAbstract: Any piecewise smooth function that is specified by an evaluation procedure involving smooth elementaPalabras claves:abs-normal form, decomposition, Karush–Kuhn–Tucker, normal growth, Piecewise linearization, projected Hessian, second-order optimality, tangential stationarityAutores:Andreas Griewank, Walther A.Fuentes:scopusEvaluating higher derivative tensors by forward propagation of univariate Taylor series
ReviewAbstract: This article considers the problem of evaluating all pure and mixed partial derivatives of some vectPalabras claves:Computational differentiation, Higher order derivativesAutores:Andreas Griewank, Utke J., Walther A.Fuentes:scopusADOL-C: Computing higher-order derivatives and sparsity pattern for functions written in C/C++
Conference ObjectAbstract: This paper presents ADOL-C, a software package for the Automatic Differentiation of C and C++ codes.Palabras claves:Automatic differentiation, Forward mode, Higher-order derivatives, Reverse mode, Sparsity detectionAutores:Andreas Griewank, Walther A.Fuentes:scopusCharacterizing and testing subdifferential regularity in piecewise smooth optimization
ArticleAbstract: Functions defined by evaluation programs involving smooth elementals and absolute values as well asPalabras claves:abs-normal form, Clarke generalized gradient, First-order-convexity, Linear independence kink qualification, Mangasarin–Fromovitz kink qualification, Mordukhovich subdifferential, Subdifferential regularityAutores:Andreas Griewank, Walther A.Fuentes:scopusAn algorithm for nonsmooth optimization by successive piecewise linearization
ArticleAbstract: We present an optimization method for Lipschitz continuous, piecewise smooth (PS) objective functionPalabras claves:abs-normal form, Algorithmic differentiation, Clarke stationary, Nonsmooth optimization, Piecewise smoothnessAutores:Andreas Griewank, Fiege S., Walther A.Fuentes:scopusBeyond the oracle: Opportunities of piecewise differentiation
Book PartAbstract: For more than 30 years much of the research and development in nonsmooth optimization has been prediPalabras claves:Autores:Andreas Griewank, Walther A.Fuentes:scopusAlgorithm 799: Revolve: An implementation of checkpointing for the reverse or adjoint mode of computational differentiation
ArticleAbstract: In its basic form, the reverse mode of computational differentiation yields the gradient of a scalarPalabras claves:Adjoint mode, ALGORITHMS, Checkpointing, Computational differentiation, Reverse modeAutores:Andreas Griewank, Walther A.Fuentes:scopusAlgorithmic differentiation for piecewise smooth functions: a case study for robust optimization
ArticleAbstract: This paper presents a minimization method for Lipschitz continuous, piecewise smooth objective functPalabras claves:90C26, 90C30, 90C47, Algorithmic differentiation, Nonsmooth optimization, Piecewise linearization, Robust optimizationAutores:Andreas Griewank, Fiege S., Kulshreshtha K., Walther A.Fuentes:scopus