Enrollment year
2020/2021
Academic discipline
MAT/08 (NUMERICAL ANALYSIS)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Curriculum
PERCORSO COMUNE
Period
2nd semester (01/03/2021 - 11/06/2021)
Lesson hours
24 lesson hours
Prerequisites
Standard courses of Mathematical Analysis and Numerical Analysis
Learning outcomes
The course offers an overview of the theory and applications of Optimization, showing the main results and their aplication to concrete problems arising fro the applications.
Course contents
1. Introduction to Optimization methods. Matlab Optimization Toolbox.
2. Derivative – free methods: Nelder – Mead.
3. Newton method.
4. Descent methods (line search):
- stepsize selection, Wolfe conditions, backtracking.
- Newton direction.
- Quasi – Newton directions(rank 1 update, DFP and BFGS methods)
- Gradient direction.
- Conjugate gradient (methods of Fletcher – Reeves, Polak – Ribiere, Hestenes – Stiefel).
5. Trust – Region methods.
6. Nonlinear Least – Square:
- Gauss – Newton.
- Levenberg - Marquardt.
7. Application to neural networks and Deep Learning.
Teaching methods
Lectures and Matlab laboratory
Reccomended or required readings
Nocedal, Jorge; Wright, Stephen J. Numerical optimization. Second edition. Springer, 2006.
Assessment methods
Final project, presentation and oral examination
Sustainable development goals - Agenda 2030
Università di Pavia - Offerta formativa