Function with many local minima

Old Monk

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.

AlephZero

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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Old Monk	Function with many local minima Tweet 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.

AlephZero $Math 2012$ Recognitions: Science Advisor	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)##