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

To pass the exam the student has two options: 

1) participate to intermediate written and lab verifications. At the end of the teaching, the student may decide to take an oral exam to improve her/his mark.

2) participate to an oral exam at the end of the teaching on the entire content of the course. ​

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements 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).