Mathematical optimization is more and more important in engineering techniques. Today the computational power allows engineer to solve digitally wide-ranging optimization problems. The course purpose is to provide basic notions in the optimization field in order to learn usual methods and theirs practical uses. At the end of the course, the students will know optimization basis. He will be able to choose and use an optimization method to any given problem, whether it is linear or non-linear, with or without constraints, of small or big size.