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A variety of generalizations of the concept of the derivative to classes of continuous nondifferentiable functions have been proposed. Likewise, algorithms for nondifferentiable equation solving and optimization assume the ability to evaluate some element of a generalized derivative at points visited by the algorithm. However, not all generalized derivatives are equal in the sense that the particular generalized derivative element employed can have a large influence on the performance of algorithms. This leads to the notion of computationally relevant generalized derivatives. Until recently, it has not been possible to evaluate generalized derivative elements without an (often arduous) manual analysis of specific cases. Furthermore, in settings such as implicit functions, parametric ordinary differential equations and parametric optimization problems, results enabling the evaluation of concrete, computationally relevant generalized derivatives have not been available. This talk will discuss a number of new theoretical results and algorithms that lead to automatic methods for the evaluation of computationally relevant generalized derivatives in several settings. We will also outline important applications where these advances are having an enabling impact on simulation, sensitivity analysis and optimization.
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Journal of Global Optimizationno. 2 (2024): 1-24
Energypp.131524, (2024)
Journal of Mathematical Analysis and Applicationspp.128257, (2024)
arXiv (Cornell University)no. 1 (2023): 1-46
Matthew R Billingsley,Paul I Barton
arXiv (Cornell University) (2021)
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