Numerical Methods and Optimization

Section outline

• Select section General

  General

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  Matlab license updated

  See https://elearning.di.unipi.it/mod/forum/discuss.php?d=1230 for information on how to update the license file and continue using Matlab with the university's license in 2017.
  

  • Select activity Forum News

    

    Forum News
• Select section Office hours before next exam

  Office hours before next exam

  Not available
• Select section Course Schedule

  Course Schedule

  Tuesday 9:00 - 11:00 room L1
  

  Tuesday 16:00 - 18:00 room H
  

  Wednesday 11:00 - 13:00 room C
  

  Thursday 11:00 - 13:00 room C

  Instructors

  Mauro Passacantando
  

  Room 323, Tel. 050 2212756, e-mail: mauro.passacantando@unipi.it
  

  Federico Poloni

  Room 343, Tel. 050 2213143, e-mail: federico.poloni@unipi.it
  Office hours (during the course): Monday 14:00-16:00

  Review seminars

  Dr. Stefano Massei (SNS) will hold 8 additional exercise sessions containing a review of the course prerequisites (calculus, linear algebra and numerical analysis). They are held on Wednesday at 14:00 in room A1. They are meant to ensure that everyone is familiar with the same background material irrespective of their bachelor studies. These lectures do not contain material included in the exam syllabus, and they can be skipped if you are already familiar with these topics from your past courses.
  
• Select section Program

  Program

  Syllabus

  Program

  Detailed lecture reports These reports are updated regularly after the lectures and describe in detail the material that has been covered in each of them. They are the most reliable source to know what has actually been covered in the course.
  
• Select section Textbooks

  Textbooks

  For the optimization part:
  

  • S. Boyd, L. Vandenberghe, Convex optimization, Cambridge University Press, 2004
  • M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear programming: theory and algorithms, Wiley & Sons, 2006 (Chapters 1-6, 8-9)
  • J. Nocedal, S. Wright, Numerical Optimization, Springer Series in Operations Research and Financial Engineering, 2006 (Chapters 1-3, 5, 12, 16, 17)
  • A.R. Conn, K. Scheinberg, L.N. Vicente, Introduction to Derivative-Free Optimization, SIAM series on Optimization, 2009 (Chapters 1, 7)

  For the numerical linear algebra part:
  

  • J. Demmel, Applied Numerical Linear Algebra, SIAM press 1996
  • L. N. Trefethen, D. Bau, Numerical Linear Algebra, SIAM press 1997 (alternative)
    

  
  
• Select section Slides and support files (optimization part)

  Slides and support files (optimization part)

  • Introduction to the course

  • Topology and calculus background

  • Convex sets and convex functions

  • Unconstrained optimization  --  Exercises on unconstrained optimization

  • Constrained optimization  --  Exercises on constrained optimization

  • Support Vector Machines for classification problems  --  svm1.txt  --  svm2.txt  --  svm3.txt
    
• Select section Slides and support files (linear algebra part)

  Slides and support files (linear algebra part)

  • Select activity Exercises on Matlab syntax

    

    Exercises on Matlab syntax File
  • Select activity Definiteness of matrices - definitions and characterization

    

    Definiteness of matrices - definitions and characterization File
  • Select activity Exercises on Householder reflectors and QR factorization

    

    Exercises on Householder reflectors and QR factorization File
  • Select activity Lab assignments on QR factorization (updated on 2016-10-5: fixed a couple of errors)

    

    Lab assignments on QR factorization (updated on 2016-10-5: fixed a couple of errors) File
  • Select activity Lab assignments on linear systems

    

    Lab assignments on linear systems File
  • Select activity Example matrix (karate_ascii.mat)

    

    Example matrix (karate_ascii.mat) File
  • Select activity Lab assignments on least squares problems

    

    Lab assignments on least squares problems File
  • Select activity Stats and salaries data (salaries.csv)

    

    Stats and salaries data (salaries.csv) File
  • Select activity Lab assignments on eigenvalue problems

    

    Lab assignments on eigenvalue problems File
  • Select activity Exercises on the Schur factorization (theoretical)

    

    Exercises on the Schur factorization (theoretical) File
• Select section Lecture recordings (linear algebra part)

  Lecture recordings (linear algebra part)

  Theory lectures:

  The lectures held in Room C will appear online on http://mediateca.unipi.it/category/metodi-numerici-ed-ottimizzazione-2016/60. There is a delay of a few days because of post-production of the videos by the e-learning team.
  
  The handwritten PDF files are uploaded on https://owncloud.dev.unipi.it/index.php/s/LVoYlumOV8cBEpL shortly after each lecture.
  
  

  Lab lectures:

  Screencast are available on http://pages.di.unipi.it/fpoloni/files/nmo16/.
  
• Select section Matlab files

  Matlab files

  The computer lab activities will be performed using MATLAB. Students of the University of Pisa can install MATLAB free of charge with the university's license. Instructions on http://doc.sid.unipi.it/images/1/17/Istruzioni_Installazione_MatLab_Student.pdf (instructions in Italian only, sorry, but with lots of pictures).

  Linear algebra part

  • Select activity matlab cheat sheet

    

    matlab cheat sheet File
  • Select activity householder reflector construction

    

    householder reflector construction File
  • Select activity Arnoldi process

    

    Arnoldi process File
  • Select activity QR factorization (uses the Householder reflector in the previous file)

    

    QR factorization (uses the Householder reflector in the previous file)
• Select section Matlab files (optimization part)

  Matlab files (optimization part)

  • Select activity Gradient method for quadratic functions

    

    Gradient method for quadratic functions File
  • Select activity Gradient method with inexact line search

    

    Gradient method with inexact line search File
  • Select activity Objective function used in the gradient method

    

    Objective function used in the gradient method File
  • Select activity Conjugate gradient method for quadratic functions

    

    Conjugate gradient method for quadratic functions File
  • Select activity Directional direct-search method

    

    Directional direct-search method File
  • Select activity Newton method with inexact line search

    

    Newton method with inexact line search File
  • Select activity Frank-Wolfe method

    

    Frank-Wolfe method File
  • Select activity Penalty method

    

    Penalty method File
  • Select activity Objective function used in the penalty method

    

    Objective function used in the penalty method File
  • Select activity Logarithmic barrier method

    

    Logarithmic barrier method File
  • Select activity Objective function used in the Logarithmic barrier method

    

    Objective function used in the Logarithmic barrier method File
  • Select activity svm1

    

    svm1 File
  • Select activity svm2

    

    svm2 File
  • Select activity svm3

    

    svm3 File
• Select section Other study material

  Other study material

  • Select activity Linear algebra recall and special matrices (prof. Bevilacqua's notes)

    

    Linear algebra recall and special matrices (prof. Bevilacqua's notes) File
  • Select activity Eigenvalues (prof. Bevilacqua's notes)

    

    Eigenvalues (prof. Bevilacqua's notes) File
  • Select activity Matrix norms (prof. Bevilacqua's notes)

    

    Matrix norms (prof. Bevilacqua's notes) File

    Some notes written by prof. Roberto Bevilacqua, former teacher of this course. They contain useful background material on linear algebra as well as some of the new content explained in the first lectures.
    

  • Select activity Student notes 2010-2011 course (Italian)

    

    Student notes 2010-2011 course (Italian) File

    The students of the 2010-2011 edition of NMO produced a set of notes written in LaTeX (in Italian) and released them under a CC license. The program of the course has changed since then, but the notes may still be useful.
    

  • Select activity Short note on identity-plus-rank-one matrices

    

    Short note on identity-plus-rank-one matrices File
  • Select activity Answers to a few questions asked by a student

    

    Answers to a few questions asked by a student File
  • Select activity More answers to questions asked by a student

    

    More answers to questions asked by a student File
  • Select activity More answers to student questions

    

    More answers to student questions File
• Select section Exams

  Exams

  • Written exam: January 16  --  Marks
    

  • Written exam: February 8 -- Marks

  • Written exam: April 11  --  Marks
    

  • Written exam: June 13 -- Marks

  • Written exam: July 3 -- Marks
    

  • Written exam: July 24 -- Marks
    

  • Written exam: September 11 -- Marks

  • Written exam: October 30 -- Marks
    

  • Oral exam: October 31, 15:00, room N1
    

  • Select activity Practice test (mock exam) 2016-12-13

    

    Practice test (mock exam) 2016-12-13 File