dc.contributor.author | Gower, R. M. | |
dc.contributor.author | Gower, A. L. | |
dc.date.accessioned | 2018-09-20T16:09:32Z | |
dc.date.available | 2018-09-20T16:09:32Z | |
dc.date.issued | 2014-10-29 | |
dc.identifier.citation | Gower, R. M. Gower, A. L. (2014). Higher-order reverse automatic differentiation with emphasis on the third-order. Mathematical Programming 155 (1), 81-103 | |
dc.identifier.issn | 0025-5610,1436-4646 | |
dc.identifier.uri | http://hdl.handle.net/10379/11704 | |
dc.description.abstract | It is commonly assumed that calculating third order information is too expensive for most applications. But we show that the directional derivative of the Hessian () can be calculated at a cost proportional to that of a state-of-the-art method for calculating the Hessian matrix. We do this by first presenting a simple procedure for designing high order reverse methods and applying it to deduce several methods including a reverse method that calculates . We have implemented this method taking into account symmetry and sparsity, and successfully calculated this derivative for functions with a million variables. These results indicate that the use of third order information in a general nonlinear solver, such as Halley-Chebyshev methods, could be a practical alternative to Newton's method. Furthermore, high-order sensitivity information is used in methods for robust aerodynamic design. An efficient high-order differentiation tool could facilitate the use of similar methods in the design of other mechanical structures. | |
dc.publisher | Springer Nature | |
dc.relation.ispartof | Mathematical Programming | |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Ireland | |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/ie/ | |
dc.subject | automatic differentiation | |
dc.subject | high-order methods | |
dc.subject | tensors vector products | |
dc.subject | hessian matrix | |
dc.subject | sensitivity analysis | |
dc.subject | unconstrained optimization | |
dc.subject | halley methods | |
dc.subject | derivatives | |
dc.subject | computation | |
dc.subject | hessians | |
dc.title | Higher-order reverse automatic differentiation with emphasis on the third-order | |
dc.type | Article | |
dc.identifier.doi | 10.1007/s10107-014-0827-4 | |
dc.local.publishedsource | http://arxiv.org/pdf/1309.5479 | |
nui.item.downloads | 0 | |