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Characterizing 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:scopusA method for pointwise evaluation of polyconvex envelopes
ArticleAbstract: We investigate a method for computing the value of a polyconvex envelope at a given feed A<sup>0</suPalabras claves:General position, optimization, Polyconvex envelopes, Stability testAutores:Andreas Griewank, Bosse T., Eneya L.Fuentes:scopusSolving piecewise linear systems in abs-normal form
ArticleAbstract: With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solutioPalabras claves:coherent orientation, Complementary system, Generalized Jacobian, Partial contractivity, Semismooth Newton, Sign real spectral radius, Switching depthAutores:Andreas Griewank, Bernt J., Radons M., Streubel T.Fuentes:scopusStarlike domains of convergence for Newton's method at singularities
ArticleAbstract: Given a solution x<sup>*</sup> of a system of nonlinear equations f with singular Jacobian ∇f(x<sup>Palabras claves:Subject Classifications: AMS(MOS): 65H10, CR: 5.15Autores:Andreas GriewankFuentes: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:scopusThe approximate solution of defining equations for generalized turning points
ArticleAbstract: A set of defining equations for turning points is shown to produce a test function that can be compuPalabras claves:Newton's method, Singularities, Turning pointsAutores:Andreas Griewank, Reddien G.Fuentes:scopusThe approximation of generalized turning points by projection methods with superconvergence to the critical parameter
ArticleAbstract: A procedure is given that generates characterizations of singular manifolds for mildly nonlinear mapPalabras claves:Subject Classifications: AMS (MOS): 65H10, CR: G1.5Autores:Andreas Griewank, Reddien G.Fuentes:scopusAutomated extension of fixed point PDE solvers for optimal design with bounded retardation
Book PartAbstract: We study PDE-constrained optimization problems where the state equation is solved by a pseudo-time sPalabras claves:Aerodynamic shape optimization, Augmented Lagrangian, Automatic differentiation, Climate model, Exact penalty function, Fixed point solvers, Nonlinear optimization, parameter optimizationAutores:Andreas Griewank, Gauger N.R., Hamdi A., Kratzenstein C., Özkaya E., Slawig T.Fuentes:scopusCubic 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:scopusConstrained optimization and optimal control for partial differential equations
BookAbstract: This special volume focuses on optimization and control of processes governed by partial differentiaPalabras claves:Autores:Andreas Griewank, Engell S., Hinze M., Leugering G., Rannacher R., Schulz V., Ulbrich M., Ulbrich S.Fuentes:scopus