# 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