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One-sided directional derivative and applications
Computing, 1975In this paper certain theorems establishing the existence of onesided directional derivative for some classes of functions are proved. These theorems are then applied to problems of best approximations.
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Communication Lower Bounds Using Directional Derivatives
Journal of the ACM, 2013We study the set disjointness problem in the most powerful model of bounded-error communication, the k -party randomized number-on-the-forehead model. We show that set disjointness requires Ω(√n/2 k k ) bits of communication, where n
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Directional Derivatives of Marginal Functions
2002Let X = R n , Y = R m and let U be a compact set in Y. We consider the functions $$\begin{array}{*{20}{c}} {\varphi \left( x \right) = \inf \left\{ {f\left( {x,y} \right)\left| {y \in U} \right.} \right\},} \\ {\Phi \left( x \right) = \sup \left\{ {f\left( {x,y} \right)\left| {y \in U} \right.} \right\},} \end{array}$$ where f : X × Y → R is ...
Bernd Luderer +2 more
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Liénard’s Generalisation: A Direct Derivation
Resonance, 2018In this pedagogical article, we elucidate the direct derivation of total power emitted by an accelerating charged particle, known as Lienard’s generalisation, using differentiation under integral sign technique.
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Directional derivatives of quasiconvex functionals
Journal of Soviet Mathematics, 1988We show that a directional derivative of a quasiconvex functional is also a quasiconvex functional. In this connection we study properties of quasiconvex and positively homogeneous functionals.
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New concepts of directional derivatives for set-valued maps and applications to set optimization
Optimization, 2023Marius Durea, Radu Strugariu
exaly