Abstract
In several situations, we are interested in computing the range not only of a specific function, but also its derivative(s). This is the case for virtually all problems considered in this book: for optimization problems, nonlinear equations, seeking Pareto-sets of multicriteria problems, etc.; shortly: whenever we need to apply the interval Newton operator or enforce box-consistency (or use other similar tools). This chapter reviews main manners to bound the derivatives; the focus is on algorithmic differentiation, which turned out to be a very useful tool and (unlike, e.g., using finite-differences) it is compatible with the interval analysis. The author’s library ADHC is briefly presented.
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Kubica, B.J. (2019). Bounding Derivatives by Algorithmic Differentiation. In: Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems. Studies in Computational Intelligence, vol 805. Springer, Cham. https://doi.org/10.1007/978-3-030-13795-3_3
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DOI: https://doi.org/10.1007/978-3-030-13795-3_3
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