
Dettaglio Insegnamento
Anno Accademico 
2021/2022 
Corso di Studi 
Dott.  MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering 
Anno di Corso 
1 
Codice Identificativo 
057413 
Denominazione Insegnamento 
NUMERICAL OPTIMAL CONTROL IN ENGINEERING, FINANCE AND QUANTUM MECHANICS 
Tipo Insegnamento 
MONODISCIPLINARE 
Crediti Formativi Universitari (CFU) 
5.0 
Programma sintetico 
The mission of the course is the transfer of a general methodology to correctly formulate largescale optimal control problems at the algebraic level. This algebraic formulation is crucial to identifying appropriate numerical solution strategies among the most modern ones proposed in the literature. To this end, several optimal control problems from application fields such as engineering, finance, and quantum mechanics will be considered and used in handson laboratory sessions.
Part 1  Optimal control of PDEs (about 6 hours):
1.1 Formulation of PDEconstrained optimal control problems
1.2 Examples:
 Heat conductive systems (Parabolic PDEs)
 Stationary heat conductive systems (Elliptic PDEs)
 Optimal flow control (Stokes  NavierStokes stationary)
 FokkerPlanck equation (Finance)
 Quantum systems (Control of electrons  Schrödinger equation)
1.3 Formulation of optimality systems (KKT, reduced gradient, reduced Hessian)
Part 2  Optimization based blackbox approaches (about 9 hours):
2.1 Steepest descent and projected gradient methods
2.2 Newton and projected Newton methods
2.3 Monotonic schemes for problems characterized by concave cost functions
2.4 MGOPT
Part 3  Allatonce strategies (about 9 hours):
3.1 Sequential quadratic programming
3.2 Multigrid methods for KKT systems
3.3 Preconditioning for KKT systems 
Settori Scientifico Disciplinari (SSD) 


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Ciaramella Gabriele


