Optimisation problems with ODE/PDE constraints
Tutor / directorMuñoz Romero, José
Document typeBachelor thesis
Rights accessOpen Access
Optimisation problems are used to find the best solution from all the possible ones, usually with some constraints. If this constraints are related with physics, it is very common to use differential equations to describe the phenomenon. This project aims to study this type of problems and their applications.To construct a system of equations, we will use the adjoint equations to differentiate the problem and different discretisations to obtain the system. Next, we will choose from different methods to solve it, such as the conjugate gradient and the GMRES (Generalised minimal residual method). We will apply these steps to two versions of the parachute problem, a linear and a non-linear one. Finally, we will analyse which methods are more suitable.
SubjectsCalculus of variations, Mathematical optimization, Càlcul de variacions, Optimització matemàtica
DegreeGRAU EN MATEMÀTIQUES (Pla 2009)