UE Numerical optimisation

This program combines case studies coming from real life problems or models and lectures providing the mathematical and numerical backgrounds.

Contents:

• Introduction, classification, examples.
• Theoretical results: convexity and compacity, optimality conditions, KT theorem
• Algorithmic for unconstrained optimisation (descent, line search, (quasi) Newton)
• Algorithms for non differentiable problems
• Algorithms for constrained optimisation: penalisatio, SQP methods
• Applications

Basic algebra (linear spaces, matrix computation) Basic calculus (Norm, Banach spaces, Hilbert spaces, basic differential calculus) The students should be able to compute the gradient and the Hessian of real functions on IR^n and also differentials of simple functions such as quadratic forms.

Recognise and classify optimisation problems

Solve optimisation problems using adequate algorithms and methods

Practical implementation