ECTS - University of Pisa
| Modules | Area | Type | Hours | Teacher(s) | |
| OPTIMIZATION METHODS | MAT/09 | LEZIONI | 60 |
|
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.
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.
At the end of the course the student will be able to use the MATLAB software for solving optimization and equilibrium problems.
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.
Students can acquire the ability to formulate, analyse and solve optimization and equilibrium problems
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.
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:
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:
The examination consists of a written test and an 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.
