The course intends to deepen the understanding of optimization theory with a geometric approach, and to introduce in a second part the study of dynamical systems.
I. Optimization with mixed constraints a. Tangent cone and KKT conditions b. Mixed constraints problem c. Constraints qualification conditions d. Convex problems e. Saddle point and duality
II. Dynamical systems a. Introduction b. Systems of linear equations
- Constant coefficient : resolution, exponantial of matrices
- Dynamic of the solutions : steady state, stability, planar systems
- nonhomogeneous systems c. Systems of nonlinear differential equations
- Existence and uniqueness theorem
- Linearized system, Hartman-Grobman theorem