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On a lecture note I read about Calculus of Variations

faculty.uml.edu/cbyrne/cov.pdf

the author talks about Euler-Lagrange equation, then continues to say "unfortunately, many times a closed form solution [for EL eqn] is not known. One way to cope with this problem is to use a gradient descent technique. Incidentally, the left hand side of the Euler-Lagrange equation can be regarded as an infinite-dimensional gradient".

How did he make this transition, from a EL PDE to gradient descent? Which class, book would cover this subject? My books on Calculus of Variations have nothing on this. Should I look under Optimization, Numerical PDE?

Thanks,

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    @gnometorule the PDF here says the same thing, using the Luenberger book - http://hci.iwr.uni-heidelberg.de/Staff/bgoldlue/fvia_ws_2011/fvia_ws_2011_01_variational_analysis.pdf. I guess I need to understand Functional Analysis in order to proceed on this path.2012-01-01

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