# Function with many local minima

1. Dec 16, 2012

### 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.

2. Dec 17, 2012

### 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 $\sin(1/x)$