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Cubic overestimation and secant updating for unconstrained optimization of C 2, 1 functions
ArticleAbstract: The discrepancy between an objective function f and its local quadratic model f(x)+ f(x) s+s H(x) s/Palabras claves:compromise update, cubic overestimation, eigenvalue decomposition, Quasi-Newton, unconstrained optimizationAutores:Andreas Griewank, Bosse T., Fischer J., Jonathan FischerFuentes:scopusDerivative Convergence for Iterative Equation Solvers
ArticleAbstract: When nonlinear equation solvers are applied to parameter-dependent problems, their iterates can be iPalabras claves:Automatic differentiation, Derivative convergence, Implicit functions, Newton-like methods, preconditioning, Secant updatesAutores:Andreas Griewank, Bischof C., Carle A., Corliss G.F., Williamson K.Fuentes:scopusAchieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation
ArticleAbstract: In its basic form the reverse mode of automatic differentiation yields gradient vectors at a small mPalabras claves:Adjoint, Checkpointing, Complexity, Gradient, RecursionAutores:Andreas GriewankFuentes: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: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:scopusIntegrating Lipschitzian dynamical systems using piecewise algorithmic differentiation
ArticleAbstract: In this article we analyse a generalized trapezoidal rule for initial value problems with piecewisePalabras claves:65L05, 65L06, 65L70, 65L99, 65P10, Automatic differentiation, dense output, energy preservation, Lipschitz continuity, nonsmooth, Piecewise linearization, trapezoidal ruleAutores:Andreas Griewank, Hasenfelder R., Lehmann L., Radons M., Streubel T.Fuentes:scopusPiecewise linear secant approximation via algorithmic piecewise differentiation
ArticleAbstract: It is shown how piecewise differentiable functions F:ℝ <sup>n</sup> ↦ℝ <sup>m</sup> that are definedPalabras claves:49J52, 65D25, 65K10, ADOL-C, Automatic differentiation, generalized hermite interpolation, generalized Newton's method, Lipschitz continuity, stable piecewise linearizationAutores:Andreas Griewank, Hasenfelder R., Lehmann L., Radons M., Streubel T.Fuentes:scopusProperties of an augmented Lagrangian for design optimization
ArticleAbstract: We consider the task of design optimization, where the constraint is a state equation that can onlyPalabras claves:Bounded retardation, Exact penalty function, Nonlinear optimization, preconditioning, Simultaneous analysis and designAutores:Andreas Griewank, Hamdi A.Fuentes:scopusStructured second-and higher-order derivatives through univariate taylor series
ArticleAbstract: Second-and higher-order derivatives are required by applications in scientific computation, especialPalabras claves:Automatic differentiation, Computational complexity, Hessian matrices, Second-order partial derivatives, Taylor seriesAutores:Andreas Griewank, Bischof C., Corliss G.F., Dennis Schnabel J.A.R.B.Fuentes:scopus