Publication: Efficient calculation of sensitivities for optimization problems
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Efficient calculation of sensitivities for optimization problems

- Article in a journal -
 

Area
Optimization

Author(s)
Andreas Kowarz , Andrea Walther

Published in
Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Year
2007

Abstract
Sensitivity information is required by numerous applications as for example optimization algorithms, parameter estimations or real time control. Sensitivities can be computed with working accuracy using the forward mode of automatic differentiation (ad). ADOL-C is an ad-tool for programs written in C or C++. Originally, when applying ADOL-C, tapes for values, operations and locations are written during the function evaluation to generate an internal function representation. Subsequently, these tapes are evaluated to compute the derivatives, sparsity patterns etc. using the forward or reverse mode of ad. The generation of the tapes can be completely avoided by applying the recently implemented tapeless variant of the forward mode for scalar and vector calculations. The tapeless forward mode enables the joint computation of function and derivative values directly from main memory within one sweep. Compared to the original approach shorter runtimes are achieved due to the avoidance of tape handling and a more effective, i.e., joint optimization for function and derivative code. Advantages and disadvantages of the tapeless forward mode provided by ADOL-C will be discussed. Furthermore, runtime comparisons for two implemented variants of the tapeless forward mode are presented. The results are based on two numerical examples that require the computation of sensitivity information.

AD Tools
ADOL-C

AD Theory and Techniques
Forward Mode, Implementation Strategies

BibTeX
@ARTICLE{
         Kowarz2007Eco,
       title = "Efficient calculation of sensitivities for optimization problems",
       author = "Andreas Kowarz and Andrea Walther",
       year = "2007",
       journal = "Discussiones Mathematicae, Differential Inclusions, Control and Optimization",
       volume = "27",
       pages = "119--134",
       abstract = "Sensitivity information is required by numerous applications as for example
         optimization algorithms, parameter estimations or real time control. Sensitivities can be computed
         with working accuracy using the forward mode of automatic differentiation (AD). ADOL-C is an AD-tool
         for programs written in C or C++. Originally, when applying ADOL-C, tapes for values, operations and
         locations are written during the function evaluation to generate an internal function
         representation. Subsequently, these tapes are evaluated to compute the derivatives, sparsity
         patterns etc. using the forward or reverse mode of AD. The generation of the tapes can be completely
         avoided by applying the recently implemented tapeless variant of the forward mode for scalar and
         vector calculations. The tapeless forward mode enables the joint computation of function and
         derivative values directly from main memory within one sweep. Compared to the original approach
         shorter runtimes are achieved due to the avoidance of tape handling and a more effective, i.e.,
         joint optimization for function and derivative code. Advantages and disadvantages of the tapeless
         forward mode provided by ADOL-C will be discussed. Furthermore, runtime comparisons for two
         implemented variants of the tapeless forward mode are presented. The results are based on two
         numerical examples that require the computation of sensitivity information.",
       ad_area = "Optimization",
       ad_tools = "ADOL-C",
       ad_theotech = "Forward Mode, Implementation Strategies"
}


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