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.
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.
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.
Calculus for functions of several variables, linear algebra, probability
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.
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:
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
Ricevimento: By appointment wich can be fixed in person or via email : silvia.villa@unige.it
SILVIA VILLA (President)
ERNESTO DE VITO
CESARE MOLINARI (Substitute)
According to the academic calendar
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.
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).
