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An 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:scopusOn Lipschitz optimization based on gray-box piecewise linearization
ArticleAbstract: We address the problem of minimizing objectives from the class of piecewise differentiable functionsPalabras claves:abs-normal form, Algorithmic differentiation, bundle methods, Nonsmooth optimization, Piecewise linearityAutores:Andreas Griewank, Bosse T., Fiege S., Walther A.Fuentes:scopusOn the existence of convex decompositions of partially separable functions
ArticleAbstract: The concept of a partially separable function f developed in [4] is generalized to include all functPalabras claves:65F99, 65K05, 90C30, decomposition, Optimization, partial separability, Perfect Elimination, Positive Definite Matrices, sparsityAutores:Andreas Griewank, Toint P.Fuentes:scopusOn the local convergence of adjoint Broyden methods
ArticleAbstract: The numerical solution of nonlinear equation systems is often achieved by so-called quasi-Newton metPalabras claves:Adjoint based update, Automatic differentiation, nonlinear equations, Quasi-Newton methodsAutores:Andreas Griewank, Schlenkrich S., Walther A.Fuentes:scopusThe equivalence of strict convexity and injectivity of the gradient in bounded level sets
ArticleAbstract: It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradienPalabras claves:affine invariance, Convexity, generalized gradient, injectivity, supporting hyperplaneAutores:Andreas Griewank, Jongen H.T., Kwong M.K.Fuentes:scopusThe global convergence of partitioned BFGS on problems with convex decompositions and Lipschitzian gradients
ArticleAbstract: The main purpose of this paper is the extension of Powell's (1976) global convergence result to thePalabras claves:Global convergence, partial separability, partitioned updating, R-linear or R-superlinear convergence, uniform convexityAutores:Andreas GriewankFuentes:scopus