MAA209 - A First Step in Numerical Optimization (2022-2023)

Optimization problems consider the minimization or the maximization of an objective function under eventual constraints. For most complex problems and concrete applications, solutions to optimization problems cannot be found analytically. Numerical optimization algorithms are developed to approximate solutions to general problems. Efficient algorithm often rely on the computation of the gradient of the objective function. MAA209 covers several aspects of
the classical methods that are used in such problems. For instance, the gradient
methods (or steepest descent), Newton's method and quasi-Newton methods will be discussed. One key point underlined in the course is how to choose the right optimization method adapted to the problems under study. Moreover, the performance difference between gradient algorithms and algorithms using only function evaluations is underlined. An introduction to the theoretical and numerical study of optimization problem under equality and inequality constraints is given. Introductory main ideas and algorithms related to linear programming are presented. The practical sessions focus on the analysis and the implementation of the numerical algorithms presented in the course and they are taken under consideration for the grading.