Maximize the product of a set of scalar products

So suppose we have a set of vectors $ X $ and we want to approximate the maximum of the following:

$ prod_ {x in X} b cdot x $

where the components of $ b $ sum to $ 1 $

If this counts the components of each $ x $ sum to $ 1 $ as well as.

Which algorithm would you use to do this?

Sorry if it belongs to the mathematics exchange, I was stuck between the two