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| Anno Accademico |
2022/2023 |
| 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 large-scale 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 hands-on laboratory sessions.
Part 1 - Optimal control of PDEs (about 6 hours):
1.1 Formulation of PDE-constrained optimal control problems
1.2 Examples:
- Heat conductive systems (Parabolic PDEs)
- Stationary heat conductive systems (Elliptic PDEs)
- Optimal flow control (Stokes - Navier-Stokes stationary)
- Fokker-Planck equation (Finance)
- Quantum systems (Control of electrons - Schrödinger equation)
1.3 Formulation of optimality systems (KKT, reduced gradient, reduced Hessian)
Part 2 - Optimization based black-box 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 - All-at-once 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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Scaglione
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Nome
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Programma dettagliato
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Da (compreso)
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A (escluso)
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A
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ZZZZ
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Ciaramella Gabriele
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