ECTS - University of Pisa
Students are expected to acquire: some knowledge of the main techniques and methods for the solution of numerical and optimization problems; some understanding of the connections between typical techniques of numerical analysis and optimization algorithms; tools for modeling (through numerical analysis and optimization) specific problems from the following areas: regression and parameter estimation in statistics, approximation and data fitting, machine learning, data mining, image and signal reconstruction.
The student will be assessed on his/her demonstrated ability to discuss the main course contents using the appropriate terminology. During the oral exam the student must be able to demonstrate his/her knowledge of the course material together with adequate language and proper terminology. Critical awareness of the topics will be also evaluated.
Methods:
Further information:
Undergraduate courses in calculus, linear algebra, numerical analysis (recommended) and optimization (recommended).
Delivery: face to face
Learning activities:
Attendance: Advised
Teaching methods:
Il corso è tenuto in inglese, quindi si prega di fare riferimento al programma in inglese.
Linear algebra and calculus background; Unconstrained optimization and systems of equations; Direct and iterative methods for linear systems; Iterative methods for nonlinear systems; Numerical methods for unconstrained optimization; The least-squares problem; Iterative methods for computing eigenvalues; Constrained optimization and systems of equations; Lagrangian duality; Numerical methods for constrained optimization; The fast Fourier transform; Applications: regression, parameter estimation, approximation and data fitting, support vector machines, signal reconstruction; Software tools for numerical and optimization problems (MATLAB, in particular).
Lecture notes by the lecturers available to students. Recommended readings: J.W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997 R.L. Burden, J.D. Faires, Numerical Analysis, Brooks/Cole, 2011 L.N. Trefethen, D. Bau III, Numerical Linear Algebra, SIAM, 1997 J. Nocedal, S.J. Wright, Numerical Optimization, Springer, 1999 D. Bertsekas, Nonlinear Programming, Athena, 2004 M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley, 1993
Written and oral exam.
