coherent orientation – 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