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I have worked mainly on applications of AD in various areas of nonlinear scientific computing. The main thrust was a total quasi-Newton approach to nonlinear optimization, based on the theoretical observation that Jacobians and Hessians can be orders of magnitude more expensive than their products with vectors from the left or the right. However, at least for the problems in the popular test set CUTEr that is never true as their complete full Jacobians are never more than 20 times as expensive to evaluate as the underlying vector function itself. Another effort that has soft-stalled is the analysis and numerical solution of DAEs on the basis of the computational graph of the defining equation. This generalized structural analysis continues to be viewed as mathematically unsound by the DAE mainstream. Nevertheless there is hope in that the recent MANDEA proposal for a ETN in which my current university Yachay is a partner will have a broader look at structural analysis.
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Optimization Methods and Softwarepp.1-25, (2024)
Andreas Griewank, Angel Adrian Rojas Jimenez
HAL (Le Centre pour la Communication Scientifique Directe) (2020)
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Andreas Griewank, Laihua Sheng
Mathematics for Large Scale Computingpp.1-33, (2020)
Numerical Nonsmooth Optimizationpp.331-361, (2020)
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