Advanced Optimization (30h, Wed pm from 16/9, Valrose): 
Stochastic gradient descent (Robbins-Monro, 1951) is the workhorse of many statistical and probabilistic procedures. 
In particular, it is widely used in machine learning for training artificial neural networks, support vector machines. 
This course is intended to provide a mathematical foundation to this algorithm and variants of it, along with a numerical intuition of its 
behavior on practical examples. 
It will be organized in three main blocks: 
a first one giving foundation on optimization, 
a second one dedicated introducing the stochastic gradient descent algorithm, 
and a third one discussing advanced topics in stochastic optimization.