Andreas Griewank – Page 2 – Optimization Online

Solving piecewise linear equations in abs-normal form

Published: 2013/12/30

Nonsmooth Optimization coherent orientation, generalized jacobian, linear complementarity problems, semismooth newton, sign real spectral radius, switching depth, unfolded system

With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. PL models can be derived in the fashion of automatic or algorithmic differentiation as local approximations of PS functions with a second order error in the distance to a given reference point. The resulting PL … Read more

On Stable Piecewise Linearization and Generalized Algorithmic Differentiation

Published: 2012/09/05, Updated: 2012/12/30

Andreas Griewank

Nonlinear Optimization, Nonsmooth Optimization, Optimization Software Design Principles adol-c, automatic differentiation, bouligand derivative, bundle method, coherent orientation, computational graph, conical activity, directional derivative, generalized gradients and jacobians, lipschitz continuity, midpoint method, piecewise differentiability, piecewise newton, trapezoidal rule

It is shown how functions that are defined by evaluation programs involving the absolute value function (besides smooth elementals), can be approximated locally by piecewise-linear models in the style of algorithmic, or automatic, differentiation (AD). The model can be generated by a minor modification of standard AD tools and it is Lipschitz continuous with respect … Read more

A continuous model for open pit mine planning

Published: 2009/09/19

Applications - OR and Management Sciences, Global Optimization, Infinite Dimensional Optimization continuous models, functional analysis, mine planning

This paper proposes a new mathematical model for the open pit mine planning problem, based on continuous functional analysis. The traditional models for this problem have been constructed by using discrete 0-1 decision variables, giving rise to large-scale combinatorial and Mixed Integer Programming (MIP) problems. Instead, we use a continuous approach which allows for a … Read more

Adjoint Broyden a la GMRES

Published: 2007/10/29

Andreas Griewank

Sebastian Schlenkrich

Andrea Walther

Nonlinear Systems and Least-Squares adjoint based update, arnoldi process, automatic differentiation, compact storage, generalized minimal residual, nonlinear equations, quasi-newton methods

It is shown that a compact storage implementation of a quasi-Newton method based on the adjoint Broyden update reduces in the affine case exactly to the well established GMRES procedure. Generally, storage and linear algebra effort per step are small multiples of n k, where n is the number of variables and k the number … Read more