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Cubic overestimation and secant updating for unconstrained optimization of C <sup>2, 1</sup> 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.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: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: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:scopusOn constrained optimization by adjoint based quasi-Newton methods
ArticleAbstract: In this article we propose a new approach to constrained optimization that is based on direct and adPalabras claves:Constrained optimization, KKT system, Lagrangian gradient, Quasi-Newton, Secant updatingAutores:Andreas Griewank, Walther A.Fuentes:scopusOn stable piecewise linearization and generalized algorithmic differentiation
ArticleAbstract: It is shown how functions that are defined by evaluation programs involving the absolute value functPalabras claves:ADOL-C, Automatic differentiation, Bouligand derivative, bundle methods, coherent orientation, computational graph, conical activity, directional derivative, generalized gradients and Jacobians, Lipschitz continuity, midpoint method, piecewise differentiability, piecewise Newton, trapezoidal ruleAutores:Andreas GriewankFuentes:scopusOn the abs-polynomial expansion of piecewise smooth functions
ArticleAbstract: Tom Streubel has observed that for functions in abs-normal form, generalized Taylor expansions of arPalabras claves:abs-linear form, abs-normal form, absolute convergence, forward mode propagation, Moore recurrences, Nonsmooth Taylor polynomial/series, quadratic complexityAutores:Andreas Griewank, Streubel T., Tischendorf C.Fuentes:scopusOptimal r-order of an adjoint Broyden method without the assumption of linearly independent steps
ArticleAbstract: Quasi-Newton methods based on least change secant updating formulas that solve linear equations Ax=bPalabras claves:Adjoint-based update, Automatic differentiation, nonlinear equations, Quasi-Newton methods, R-orderAutores:Andreas Griewank, Schlenkrich S., Walther A.Fuentes:scopus