نتایج جستجو برای: caputo differentiability

تعداد نتایج: 4400  

Journal: :Math. Meth. of OR 2014
Oliver Stein Nathan Sudermann-Merx

This article studies continuity and directional differentiability properties of optimal value functions, in particular at boundary points of their domain. We extend and complement standard continuity results from [12] for abstract feasible set mappings under complete convexity as well as standard differentiability results from [13] for feasible set mappings in functional form under the Slater c...

2014
Sebastian Pfaff Stefan Ulbrich Günter Leugering

We consider optimal control problems governed by nonlinear hyperbolic conservation laws at junctions and analyze in particular the Fréchet-differentiability of the reduced objective functional. This is done by showing that the control-to-state mapping of the considered problems satisfies a generalized notion of differentiability. We consider both, the case where the controls are the initial and...

Journal: :SIAM Journal on Optimization 2003
Xin Chen Houduo Qi Paul Tseng

For any function f from R to R, one can define a corresponding function on the space of n × n (block-diagonal) real symmetric matrices by applying f to the eigenvalues of the spectral decomposition. We show that this matrix-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiab...

Journal: :Tokyo Journal of Mathematics 2002

Journal: :Bulletin of the Polish Academy of Sciences Mathematics 2008

Journal: :Transactions of the American Mathematical Society 1991

Journal: :Applied Mathematics and Optimization 2021

We revisit some basic concepts and ideas of the classical differential calculus convex analysis extending them to a broader frame. reformulate generalize notion Gateaux differentiability propose new notions generalized derivative subdifferential in an arbitrary topological vector space. Meaningful examples preserving key properties original are provided.

Journal: :Proceedings of the American Mathematical Society 1965

Journal: :Appl. Math. Lett. 2015
Kazufumi Ito Bangti Jin Tomoya Takeuchi

In this note, we establish the sectorial property of the Caputo fractional derivative operator of order α ∈ (1, 2) with a zero Dirichlet boundary condition.

Journal: :Formalized Mathematics 2009

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