directional derivative – Optimization Online

A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization

Published: 2017/04/23, Updated: 2018/07/19

Generalized Convexity/Monoticity, Multi-Criteria Optimization coderivative, directional derivative, optimality condition, set optimization, set-valued map

In this paper, we follow Kuroiwa’s set approach in set optimization, which proposes to compare values of a set-valued objective map $F$ respect to various set order relations. We introduce a Hausdorff-type distance relative to an ordering cone between two sets in a Banach space and use it to define a directional derivative for $F$. … 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