Function with many local minima


by Old Monk
Tags: function, local, minima
Old Monk
Old Monk is offline
#1
Dec16-12, 10:54 PM
P: 8
I've been working on a decentralized algorithm for finding local minima. Can anyone give me a few examples of mappings of the form F:R→R that have multiple local minima. I'm having problems defining neighbourhood on mappings from R2→R, so I thought I'll test it out on single variable functions first.

Thanks.
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AlephZero
AlephZero is offline
#2
Dec17-12, 12:23 AM
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Thanks
P: 6,344
Try the sum of some trig functions with no common periouds, for example
##\sin x + \cos( \sqrt 2 x) + \sin( \sqrt3 x)##.

Or if you want a cluster of local minima, throw in something like ##\sin(1/x)##


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