CdSEMBEDDED COMPUTING SYSTEMS
Codice540AA
CFU6
PeriodoSecondo semestre
LinguaInglese
| Moduli | Settore/i | Tipo | Ore | Docente/i | |
| OPTIMIZATION METHODS | MAT/09 | LEZIONI | 60 |
|
Lo studente che parteciperà al corso sarà in grado di dimostrare una solida conoscenza delle metodologie e degli algoritmi relativi alla soluzione di problemi avanzati di ottimizzazione non lineare e di equilibrio. Inoltre, acquisirà abilità nell'uso di MATLAB per risolvere problemi di ottimizzazione non lineare e di equilibrio.
The student who successfully completes the course will be able to demonstrate a solid knowledge of the methodologies and algorithms concerning solution of advanced nonlinear optimization and equilibrium problems. He/she will acquire ability in the use of MATLAB for solving nonlinear optimization and equilibrium problems.
La verifica delle conoscenze sarà oggetto della valutazione della prova scritta e del colloquio orale previsto per ogni sessione d'esame.
The examination of knowledge will be the subject of an assessment of the written examination script and the oral interview scheduled for each examination session.
Al termine del corso lo studente sarà in grado di utilizzare il software MATLAB per risolvere problemi di ottimizzazione e di equilibrio.
At the end of the course the student will be able to use the MATLAB software for solving optimization and equilibrium problems.
Durante le sessioni di laboratorio, verranno effettuati esercizi per comprendere l'uso del software MATLAB per risolvere problemi di ottimizzazione e di equilibrio. L'esame scritto, che si svolge in un'aula PC, consiste nel risolvere problemi di ottimizzazione e di equilibrio utilizzando il software MATLAB.
During the computer laboratory sessions, exercises will be carried out to understand the use of MATLAB software for solving optimization and equilibrium problems. The written test, which takes place in a PC room, consists in solving optimization and equilibrium problems using the MATLAB software.
Gli studenti potranno acquisire le capacità di formulare, analizzare e risolvere problemi di ottimizzazione e di equilibrio.
Students can acquire the ability to formulate, analyse and solve optimization and equilibrium problems.
Durante le sessioni di laboratorio e l'esame scritto, verrà valutata la capacità dello studente di analizzare e risolvere un problema di ottimizzazione o di equilibrio.
During the laboratory sessions and the written exam, the ability of the student to analyze and solve an optimization or equilibrium problem will be evaluated.
Concetti di base di algebra lineare e calcolo differenziale.
Fundamentals of Linear algebra and Calculus.
Delivery: Frontal lessons, with the help of transparencies, laboratory exercises using computer classroom PCs or students' personal PCs
Course elearning site: download teaching materials, publication of tests for home exercises
Learning activities:
- attending lectures
- individual study
Attendance: Advised
Nonlinear optimization: existence and uniqueness of optimal soluitons, optimality conditions, duality, gradient methods, Newton and quasi-Newton methods, penalization methods, barrier methods.
Multiobjective optimization: partial order, Pareto optimal solutions, optimality conditions, scalarization approach, goal method.
Non-cooperative game theory: Nash equilibrium, matrix games, pure and mixed strategies, existence of equilibria, bimatrix games, games with infinite strategies, gap and D-gap functions.
Lecture notes are available online. Recommended reading includes the following works:
- S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, 2004.
- M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley-Interscience, 2006.
- J. Nocedal, S. Wright, Numerical Optimization, Springer Series in Operations Research and Financial Engineering, 2006
- A.R. Conn, K. Scheinberg, L.N. Vicente, Introduction to Derivative-Free Optimization, SIAM series on Optimization, 2009
- D.T. Luc, Theory of Vector Optimization, Springer, 1989
- Y. Sawaragi, H. Nakayama, T. Tanino, Theory of Multiobjective Optimization, Academic Press, 1985
- M.J. Osborne, A. Rubinstein, A Course in Game Theory, MIT press, 1994
- N. Nisan, T. Roughgarden, E. Tardos, V.V. Vazirani, Algorithmic Game Theory, Cambridge University Press, 2007
The exam is made up of one written test and one oral test.
The written test consists in solving problems of optimization or equilibrium, takes place in a PC room, has a duration of 3 hours, if passed it remains valid until the end of the same exam session.
The oral test consists of an interview between the candidate and the teacher. During the oral test the candidate may be asked to resolve written exercises.