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OPTIMIZATION AND OPERATIONAL RESEARCH

CODE 108960
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 3nd year of 8760 MATEMATICA (L-35) - GENOVA
  • 6 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA
    		•
    SCIENTIFIC DISCIPLINARY SECTOR MAT/09
    TEACHING LOCATION
  • GENOVA
    		•
    SEMESTER 2° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The course will illustrate the basic tools needed to understand and use the main optimization and operationa research  algorithms, relevant to solve machine learning and inverse problems.

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The goal of the course is to provide tools for a theoretical understanding and a practical usege of linear programming and  the main convex optimization algorithms used in machine learning and inverse problems. 

    AIMS AND LEARNING OUTCOMES

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

    PREREQUISITES

    Calculus for functions of several variables, linear algebra, probability

    TEACHING METHODS

    Classes on the blackboard and labs

    SYLLABUS/CONTENT

    The course will cover the basic notions for optimization problems. It 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. 

    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

    Exam Board

    SILVIA VILLA (President)

    ERNESTO DE VITO

    CESARE MOLINARI (Substitute)

    LESSONS

    LESSONS START

    According to the academic calendar

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    To pass the exam the student have to present a short report. The student can choose one among the following options:

    1. analyze and discuss a research article on themse close to the ones studied during classes
    2. implement an algorithms presented during the classes (in some programming language)
    3. use some available code to analyze synthetic and/or real datasets and discuss the obtained results.

    ASSESSMENT METHODS

    The report preparation and its discussion are aimed at verifying the student's achievement of an independent critical reasoning capability  in the context of machine learning.

    During the report presentation, basic questions d on the topics covered by the course amy be asked.