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Dettaglio Insegnamento

Context
Academic Year 2021/2022
Name Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering
Programme Year 1

Course Details
ID Code 057413
Course Title NUMERICAL OPTIMAL CONTROL IN ENGINEERING, FINANCE AND QUANTUM MECHANICS
Course Type MONODISCIPLINARE
Credits (CFU / ECTS) 5.0
Course Description 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
Scientific-Disciplinary Sector (SSD) --

Details
Alphabetical group Professor Course details
From (included) To (excluded)
A ZZZZ Ciaramella Gabriele
manifestidott v. 1.7.0 / 1.7.0
Area Servizi ICT
23/05/2022