Publication: Algorithmic differentiation for piecewise smooth functions: a case study for robust optimization
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Algorithmic differentiation for piecewise smooth functions: a case study for robust optimization

- Article in a journal -
 

Author(s)
Sabrina Fiege , Andrea Walther , Kshitij Kulshreshtha , Andreas Griewank

Published in
Special issue of Optimization Methods & Software: Advances in Algorithmic Differentiation Optimization Methods & Software

Editor(s)
Bruce Christianson, Shaun A. Forth, Andreas Griewank

Year
2018

Publisher
Taylor & Francis

Abstract
This paper presents a minimization method for Lipschitz continuous, piecewise smooth objective functions based on algorithmic differentiation (ad). We assume that all nondifferentiabilities are caused by abs, min, and max. The optimization method generates successively piecewise linearizations in abs-normal form and solves these local subproblems by exploiting the resulting kink structure. Both the generation of the abs-normal form and the exploitation of the kink structure are possible due to extensions of standard ad tools. This work presents corresponding drivers for the ad tool ADOL-C which are embedded in the nonsmooth solver LiPsMin. Finally, minimax problems from robust optimization are considered. Numerical results and a comparison of LiPsMin with other nonsmooth optimization methods are discussed.

Cross-References
Christianson2018Sio

BibTeX
@ARTICLE{
         Fiege2018Adf,
       crossref = "Christianson2018Sio",
       author = "Sabrina Fiege and Andrea Walther and Kshitij Kulshreshtha and Andreas Griewank",
       title = "Algorithmic differentiation for piecewise smooth functions: a case study for robust
         optimization",
       journal = "Optimization Methods \& Software",
       volume = "33",
       number = "4--6",
       pages = "1073--1088",
       year = "2018",
       publisher = "Taylor \& Francis",
       doi = "10.1080/10556788.2017.1333613",
       url = "https://doi.org/10.1080/10556788.2017.1333613",
       eprint = "https://doi.org/10.1080/10556788.2017.1333613",
       abstract = "This paper presents a minimization method for Lipschitz continuous, piecewise
         smooth objective functions based on algorithmic differentiation (AD). We assume that all
         nondifferentiabilities are caused by abs, min, and max. The optimization method generates
         successively piecewise linearizations in abs-normal form and solves these local subproblems by
         exploiting the resulting kink structure. Both the generation of the abs-normal form and the
         exploitation of the kink structure are possible due to extensions of standard AD tools. This work
         presents corresponding drivers for the AD tool ADOL-C which are embedded in the nonsmooth solver
         LiPsMin. Finally, minimax problems from robust optimization are considered. Numerical results and a
         comparison of LiPsMin with other nonsmooth optimization methods are discussed.",
       booktitle = "Special issue of Optimization Methods \& Software: Advances in
         Algorithmic Differentiation",
       editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank"
}


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