1. Introduction to optimization problems : Examples, definitions. Convex sets and convex functions.
2. Unconstrained optimization. Definition of convergence rate, complexity of the algorithm
2.0. Unconstraint optimization. Linear problem, Simplex method
2.1. Unidimensional problems
2.1.1 Derivative-based optimization methods (DBO) : Newton¿s method, Secant method
2.1.2. Derivative-free optimization methods (DFO) : Mini-Max problems, Dichotomy, Fibonacci, Golden section, Brent¿s method, ¿Economic¿ methods
2.2. Multidimensional problems
2.2.1 Direct search heuristic methods : Hooke and Jeeves, Nelder ¿ Mead simplex method
2.2.2 Gradient-based method: Gradient, steepest descent, conjugate gradients, quasi-newton
3. Constrained optimization. Examples of constrains in Control.
3.1. Dual methods : Lagrange multipliers
3.2. Primary methods: Interior and exterior points
Second part taught by RTE lecturers
4. PF and Optimal Power Flow (OPF) Problems
4.1 Definition of the Optimal power flow problem in polar and rectangular coordinates
4.2 Network representation,bus types (slack, load, voltage controlled) and branches (transfomers, cables, transmission lines,..)
4.3 Conventional Power Flow as a feasibility problem (no objective function)
4.4 Formulation of the Optimal Power Flow problem
4.5 Solution methods : decoupled solution method, numerical solutions by LMI
- Gestionnaire: Ina Taralova