Numerical modelling and optimization - NUMERICAL OPTIMIZATION (2020/2021)

Course code
4S008275
Name of lecturer
Giacomo Albi
Number of ECTS credits allocated
3
Academic sector
MAT/07 - MATHEMATICAL PHYSICS
Language of instruction
English
Location
VERONA
Period
I semestre dal Oct 1, 2020 al Jan 29, 2021.

To show the organization of the course that includes this module, follow this link * Course organization

Lesson timetable

Go to lesson schedule

Learning outcomes

The aim of the first module is to deepen the knowledge and skills especially in the modern theory of dynamical systems and give the student a solid appreciation of the deep connections between mathematics and other scientific disciplines, both in terms of the mathematical problems that they inspire and the important role that mathematics plays in scientific research and industry. Mathematical software tools, and others, will be used to implement algorithms for the solution of the real world problems studied during the course. At the end of the course the student is expected to be able to complete professional and technical tasks of a high level in the context of mathematical modelling and computation, both working alone and in groups. In particular the student will be able to write a model of a real problem, to recognise the effective parameters and analyse the model and its possible implications. The second module wants to provide sufficient theoretical and numerical background for the optimal control of dynamical systems. Such problems will be developed by means of real application examples, and recent research studies. At the end of the course students will be able to decide which numerical method is suitable for the solution of some specific optimal control problems. He/She will be able to provide theoretical results on the controllability and stability of certain optimal control problem and numerical methods. He/She will be able to develop his/her own code, and capable choose the appropriate optimization method for each application shown during the course.

Syllabus

* Introduction to the theory of optimal control linear and nonlinear problems.
* Numerical methods for optimal control such as direct and indirect methods, dynamic programming, MPC.
* Continuous optimization methods: Gradient methods, quasi-Newton and Newton methods.
* Examples and exercises in Matlab.

Reference books
Author Title Publisher Year ISBN Note
A. Bressan, B. Piccoli Introduction to the Mathematical Theory of Control AIMS 2008 1-60133-002-2
Nocedal, Jorge, Stephen Wright Numerical optimization Springer Science & Business Media 2006

Assessment methods and criteria

The student is expected to demonstrate the ability to mathematically formalize and solve models used in several scientific discipline, using, adapting and developing the models and advanced methods discussed during the lectures. To that end the final evaluation will consist in a written and oral exam.

Written exam: Questions and exercises the solution could require the use of computer.
Oral exam: Project and discussion of the written exam with questions.

The subject of the project should be decided together with the teacher.