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Algorithmic 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: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: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:scopusMaintaining factorized KKT systems subject to rank-one updates of Hessians and Jacobians
ArticleAbstract: For use in a total quasi-Newton NLP code [Griewank, A. and Walther, A., 2002, On constrained optimizPalabras claves:KKT Matrix, Low-rank update, Nullspace method, QR factorization, Reduced Hessian, Total quasi-NewtonAutores:Andreas Griewank, Korzec M., Walther A.Fuentes:scopus