Numerical Optimization
A.Y. 2023/2024
Learning objectives
To present and to analyze the main algorithms for finding zeros or constrained minimum points of nonlinear functions.
Expected learning outcomes
The ability to apply, implement, and assess algorithms for finding zeros or constrained minimum points of nonlinear functions.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Zero finding and optimization. Method of successive approximations. Newton's method. Invariances of Newton's method. Local convergence. Variants of Newton's method. Constrained minima. Methods with projection. KKT conditions, Lagrange functions e saddle points. Uzawa's method. Primal-dual method of active sets.
Prerequisites for admission
Essential: Analysis and Linear Algebra. Matlab or any other programming language.
Useful: Numerical Linear Algebra.
Useful: Numerical Linear Algebra.
Teaching methods
Lectures, exercises and lab sessions.
Teaching Resources
P.G.Ciarlet, Introduction to numerical analysis and optimization, Cambridge University Press, 1989
P. Deuflhard, Newton methods for nonlinear problems, Springer, 2011
C. T. Kelley, Iterative methods for linear and nonlinear equations, SIAM, 1995
P. Deuflhard, Newton methods for nonlinear problems, Springer, 2011
C. T. Kelley, Iterative methods for linear and nonlinear equations, SIAM, 1995
Assessment methods and Criteria
The examination consists of two parts:
- the evaluation of a small project to be chosen and
- a final oral exam on personal appointment after enrollment in an "appello".
The project has to be chosen from a list that will be published at the beginning of each exam session. The project can be realized in collaboration with another person; each member of the group has to complete its exam within the validity of the given project list. The correct email submission of the project consists in a zip archive containing source codes (but no exectuable files in view of antivirus checks) and a pdf report which summarizes the obtained results on at most 5 pages; it is recommended to write the report not in collaboration. The zip archive, together with the name of the collaborator (if present), has to be sent by email two workdays before the oral exam.
In order to arrange the date of the oral exam, the student has to be enrolled in the current "appello"; it is recommended to contact the professor at least one week before the desired date. Usually, the oral exam starts with a brief discussion on the report and lasts 45 minutes. The student is invited to present a copy of its report and to prepare for questions both concerning or not the chosen project. The exam cannot be repeated with the same project.
The complete examination is passed if the report and its discussion are evaluated positively and the oral exam is successfully passed. Final marks are given using the numerical range 0-30, and will be communicated after the oral examination.
- the evaluation of a small project to be chosen and
- a final oral exam on personal appointment after enrollment in an "appello".
The project has to be chosen from a list that will be published at the beginning of each exam session. The project can be realized in collaboration with another person; each member of the group has to complete its exam within the validity of the given project list. The correct email submission of the project consists in a zip archive containing source codes (but no exectuable files in view of antivirus checks) and a pdf report which summarizes the obtained results on at most 5 pages; it is recommended to write the report not in collaboration. The zip archive, together with the name of the collaborator (if present), has to be sent by email two workdays before the oral exam.
In order to arrange the date of the oral exam, the student has to be enrolled in the current "appello"; it is recommended to contact the professor at least one week before the desired date. Usually, the oral exam starts with a brief discussion on the report and lasts 45 minutes. The student is invited to present a copy of its report and to prepare for questions both concerning or not the chosen project. The exam cannot be repeated with the same project.
The complete examination is passed if the report and its discussion are evaluated positively and the oral exam is successfully passed. Final marks are given using the numerical range 0-30, and will be communicated after the oral examination.
MAT/08 - NUMERICAL ANALYSIS - University credits: 6
Laboratories: 24 hours
Lessons: 28 hours
Lessons: 28 hours
Professors:
Fierro Francesca, Veeser Andreas
Educational website(s)
Professor(s)