Results 1 to 10 of about 61 (39)
Arithmetic subderivatives and Leibniz-additive functions [PDF]
Annales Mathematicae et Informaticae, 2019 We first introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. More generally, we then define that an arithmetic function $f$ is Leibniz-additive if there is a nonzero-valued and completely ...
Merikoski, Jorma K. +2 more
+11 more sources
Second-order conditions for spatio-temporally sparse optimal control via second subderivatives
Journal of Nonsmooth Analysis and Optimization, 2023 We address second-order optimality conditions for optimal control problems involving sparsity functionals which induce spatio-temporal sparsity patterns. We employ the notion of (weak) second subderivatives. With this approach, we are able to reproduce the results from Casas, Herzog, and Wachsmuth (ESAIM COCV, 23, 2017, p. 263-295). Our analysis yields
Nicolas Borchard, Gerd Wachsmuth
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On the Construction of Hölder and Proximal Subderivatives [PDF]
Canadian Mathematical Bulletin, 1998 AbstractWe construct Lipschitz functions such that for all s > 0 they are s-Hölder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Hölder and approximate subderivatives.
Borwein, J. M. +2 more
openaire +3 more sources
Subderivative-subdifferential duality formula
, 2016 We provide a formula linking the radial subderivative to other subderivatives and subdifferentials for arbitrary extended real-valued lower semicontinuous functions.
Marc Lassonde
+6 more sources
, 2022 In this paper, we readdress the classical topic of second-order sufficient optimality conditions for optimization problems with nonsmooth structure. Based on the so-called second subderivative of the objective function and of the indicator function associated with the feasible set, one easily obtains second-order sufficient optimality conditions of ...
Benko, Matús, Mehlitz, Patrick
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SIAM Journal on Control and Optimization, 1996 Let \(X\) be a real Banach space endowed with a bornology \(\beta\). If \(f:X\to[-\infty,+ \infty]\) is lower semicontinuous and \(f(x)
Borwein, Jonathan M., Zhu, Qiji J.
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Links between subderivatives and subdifferentials
Journal of Mathematical Analysis and Applications, 2018 Abstract We provide formulas linking the radial subderivative to other subderivatives and subdifferentials for arbitrary extended real-valued lower semicontinuous functions.
Marc Lassonde, Marc Lassonde
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Generalized arithmetic subderivative [PDF]
Notes on Number Theory and Discrete Mathematics, 2019 Pentti Haukkanen
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Climate Model Code Genealogy and Its Relation to Climate Feedbacks and Sensitivity
Journal of Advances in Modeling Earth Systems, Volume 15, Issue 7, July 2023., 2023 Abstract Contemporary general circulation models (GCMs) and Earth system models (ESMs) are developed by a large number of modeling groups globally. They use a wide range of representations of physical processes, allowing for structural (code) uncertainty to be partially quantified with multi‐model ensembles (MMEs).
Peter Kuma +2 more
wiley +1 more source
Mathematical Modeling of Real‐Time Systems Using Heun and Piecewise Methods
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 It is often said that mathematical modeling is an implementation of mathematics in real‐world problems with the aim of better understanding them, so we can say that mathematical modeling is linked to the solution of problems. Some of the essential principles and procedures of mathematical modeling are discussed using formulas and equations.
Urfa Malik Gul +3 more
wiley +1 more source