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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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    $\begingroup$ Maybe in lecture 5 of this set: vision.ucla.edu/~ganeshs/dsp_course $\endgroup$ – Elvis Dec 29 '11 at 13:08
  • $\begingroup$ this looks useful, thanks. $\endgroup$ – BBDynSys Dec 29 '11 at 13:23
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    $\begingroup$ If you are the book type, "Optimization by Vector Space Methods" by David Luenberger is a well-written classes in this field. He covers both, although I don't remember if he directly connects the two in a chapter. $\endgroup$ – gnometorule Dec 29 '11 at 16:03
  • $\begingroup$ Classic, not classes. $\endgroup$ – gnometorule Dec 29 '11 at 16:04
  • $\begingroup$ looks like a good source; there is a chapter called "optimization of functionals" which is the kind of info I was looking for. $\endgroup$ – BBDynSys Dec 29 '11 at 17:34

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