OVERVIEW

The classes aim to give students the tools and training to understand and use the main  convex optimization  and operational research algorithms. The classes present the basic theory, and it focuses on  modeling aspects and results that are useful in applications to machine learning and inverse problems.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the course is to provide the tools for theoretical understanding and practical use of the main optimization algorithms used for data analysis.

AIMS AND LEARNING OUTCOMES

At the end of the classes the students will have a working knowledge of convex optimzation and linear programming. In particular, they will have the  skills to: Recognize convex and linear programming problems,  understand and use convex and linear programming optimization algorithms, solve convex and linear programming problems in real scenarios.

PREREQUISITES

Calculus for functions of several variables, linear algebra, probability

TEACHING METHODS

Classes on the blackboard in which theoretical concepts and algorithms will be introduced from a theoretical point of view and labs where notebooks will guide the student in the implementation and the use of convex optimization and linear programming algorithms to solve real problems. 

SYLLABUS/CONTENT

The classes will cover the basic notions for optimization problems. They will cover the linear programming problem, and optimization algorithms for the minimization of smooth and nonsmooth convex functions. The course will discuss the convergence  properties of gradient descent, stochastic gradient descent and proximal gradient descent. Applications to machine learning and imaging problems will be implemented and used  during the lab sessions. 

The teaching will contribute to the following objectives and goals for the  Agenda 2030 for sustainable development:

• Goal 4. Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all
• Goal 5. Achieve gender equality and empower all women and girls

RECOMMENDED READING/BIBLIOGRAPHY

S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004

S. Bubeck, Convex Optimization: Algorithms and Complexity, https://arxiv.org/abs/1405.4980?context=cs

S. Salzo, S. Villa, Proximal Gradient Methods for Machine Learning and Imaging, 2022

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

According to the academic calendar

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

There are two examination options. The first consists of written (and laboratory) mid-term tests, which involve the application of the concepts introduced during the course. The final grade is calculated as the average of the lab report evaluations and the mid-term tests (provided all three evaluations are satisfactory). Students may choose to complete the exam with an oral test or keep the grade obtained from the written tests and laboratory work. If any of the lab reports are unsatisfactory, they must be corrected and resubmitted. If one of the written tests is unsatisfactory, the student may choose either to take an oral test on the failed part or to take an oral exam covering the entire syllabus.

The second option consists of a single oral exam at the end of the course covering the entire syllabus, in addition to the submission of all lab reports.

Students with certified learning disabilities (DSA), disabilities, or other special educational needs are advised to contact the instructors at the beginning of the course to arrange teaching and examination methods that, while respecting the learning objectives, take into account individual learning needs and provide appropriate compensatory tools.

ASSESSMENT METHODS

The written  and the oral exam contain exercises and theoretical questions on the topics covered by the teaching, and will require the comprehension and the ability to use the introduced concepts and algorithms. The lab exam will be a guided  implementation and  use of the algorithms introduced in theoretical classes (notebooks will be used). 

FURTHER INFORMATION

Please contact the instructor for any additional information not included in the teaching description.