Computational Mathematics for Learning and Data Analysis
Timetable

Wed 9:00 – 11:00 room L1

Thu 11:00 – 13:00 room HLab

Fri 9:00 – 11:00 room N1
Lecturers
 Antonio Frangioni: office hours Tuesday 11  13
 Federico Poloni: office hours Friday 1113
Recap seminars
The
university offers the opportunity, for the interested students, to
attend a series of seminars for realignment, recap, and exercises on
basic topics of undergraduate mathematics that are useful to follow this
course (calculus, linear algebra...). They are meant to act as
realignment for those students who do not have encountered them in their
undergraduate studies.
The teacher who will hold them is
 Leonardo Robol: Friday 1618.
The first seminar of the series will be held in room X1 on Friday 29 September. The room for the next ones is still to be determined.
Lectures log (link)
Aim of the course
The course aims at providing the mathematical foundations for some of the main computational approaches to Learning, Data Analysis and Artificial Intelligence. These comprise techniques and methods for the numerical solution of systems of linear and nonlinear equations and related problems (e.g., computation of eigenvalues), as well as methods for the solution of constrained and unconstrained optimization problems. This requires the understanding of the connections between techniques of numerical analysis and optimization algorithms. The course focuses on presenting the main algorithmic approaches and the underlying mathematical concepts, with attention to the implementation aspects. Hence, use of typical mathematical environments (e.g., Matlab and Octave) and available solvers/libraries is discussed throughout the course.
Programme
 Linear algebra and calculus background
 Unconstrained optimization and systems of equations
 Direct and iterative methods for linear systems and leastsquares
 Numerical methods for unconstrained optimization
 Iterative methods for computing eigenvalues
 Constrained optimization and systems of equations
 Duality (Lagrangian, linear, quadratic, conic, Fenchel's, ...)
 Numerical methods for constrained optimization
 Software tools for numerical computations (Matlab, Octave, \ldots)
 Sparse hints to AI/ML applications
Bibliography
Slides and software by the lecturers
available to students. Useful books:
 L. N. Trefethen, D. Bau, Numerical Linear Algebra, SIAM, 1997
 J. Demmel, Applied Numerical Linear Algebra, SIAM, 1996
 S. Boyd, L. Vandenberghe, Convex optimization, 2004
 M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear programming: theory and algorithms, Wiley & Sons, 2006
 J. Nocedal, S. Wright, Numerical Optimization, Springer Series in Operations Research and Financial Engineering, 2006