66736 - Numerical Methods

Learning outcomes

At the end of the course, the student has the theoretical and practical instruments for the solution of some applicative problems and is able to analyze the obtained results.

Course contents

1.      Numerical methods for unconstrained optimization

Problem formulation, optimality conditions, examples. Descent methods: the gradient method, the steepest descent method and the Newton method. The conjugate direction method and Conjugate Gradient method. Application to nonlinear least squares problems. Line search strategies.

2.      Intoduction to constrained optimization

Problem formulation, optimality conditions, examples. Feasible direction methods and projected gradient method. Convergence analysis.

3.      Image restoration problems

The linear model of image formation (blurring and noise). Formulation of the image restoration problem as an optimization problem. Brief notes on Fourier analysis. Iterative and statistical methods.

Readings/Bibliography

• J. Nocedal, S. Wright, Numerical Optimization, Springer, 1999
• P. C. Hansen, J. G. Nagy, D. P. O'Leary, Deblurring Images: Matrices, Spectra, and Filtering, SIAM
  

Teaching methods

Lessons and exercises in the computer laboratory

Assessment methods

The oral examination is a discussion of  a project chosen among some proposed projects. The oral examination is aimed at evaluating the ability of the student to solve numerical problems on the computer and to critically analyze the obtained results.

Teaching tools

Slides of the teacher

Office hours

See the website of Germana Landi