Monetary policy optimization I was wondering if anyone could give me some advice / lectures / introduction to stochastic optimization that could be applied to monetary policy. I have heard of the Dynamic stochastic general equilibrium modeling (DSGE) but I think that this is more linked to the consumer theory and not really to monetary policy. Correct me if I am mistaking ... 

Also, I am familiar with convexity and linear optimization, but a little bit shaky when it comes to stochastic optimization. Therefore I would welcome the opportunity to also get some recommendations on that if you have some, in order to deepen my understanding of it !
You are unfortunately mistaken. DSGE models are at the heart of monetary policy and the most widely used class of models in this field. To work in monetary there is no real way around learning DSGE.

A very good book to get started. is Walsh (2010) "Monetary Theory and Policy". I can also recommend Gali's book ("Monetary Policy, Inflation, and the Business Cycle", 2008), but he skips a lot of steps. These will give you a very good introduction to DSGE.

The mother of all books on monetary policy is "Interest and Prices:
Foundations of a Theory of Monetary Policy" by Woodford, but can be hard to read at times. I would start with Walsh.

Note that there are small, medium and large scale models. You can pretty much forget about large scale ones. I recommend starting to study small scale models. The small scale model should boil down to three equations and much of the intuition for it can even be understood from old keynesian type models such as IS-LM and AS-AD. You should also be familiar with basic Solow-Growth models.