Numerical Optimization

A.Y. 2021/2022
Overall hours
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.
Course syllabus and organization

Single session

Lesson period
Second semester
Assessment methods and critera for its result
The assessment methods and critera for its results will not been changed, except for the fact that the final oral exam will be in person or on Microsoft Teams according to the existing directives in force at the time of the exam.

Course structure
More specific information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation.

The course syllabus will not be changed.
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.
Teaching methods
Lectures, exercises and lab sessions.
Teaching Resources
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.
MAT/08 - NUMERICAL ANALYSIS - University credits: 6
Laboratories: 24 hours
Lessons: 28 hours
on appointment by email
Skype or Microsoft Teams