2024
Functional Optimization
Name: Functional Optimization
Code: MAT14359M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Presentation
Human beings always try to optimize what they have. The same happens in nature (e.g. light, according to Fermat's principle, travels the shortest path between two points). In this course we deal with optimization of functionals, which are functions defined in infinite dimensional spac
Sustainable Development Goals
Learning Goals
Objective:
- Basic formation in functional optimization with the aim of developing the knowledge of students in this area or its use in other areas of mathematics, physics, economics, etc.
Skills and competencies:
- Develop abstract thought as a means of solving, with both greater generality & simplicity, specific problems of other areas, e.g.. economics, engineering, biology, mechanics, optics, etc.
- Abstraction skills, creative intuition, model construction and spirit of criticism.
- Skills for explaining the obtained results, both orally and written.
- Basic formation in functional optimization with the aim of developing the knowledge of students in this area or its use in other areas of mathematics, physics, economics, etc.
Skills and competencies:
- Develop abstract thought as a means of solving, with both greater generality & simplicity, specific problems of other areas, e.g.. economics, engineering, biology, mechanics, optics, etc.
- Abstraction skills, creative intuition, model construction and spirit of criticism.
- Skills for explaining the obtained results, both orally and written.
Contents
- Introduction. Classical exemples (brachistochrone, Newtons problem of minimal resistance,
).
- Prerequisites of Functional Analysis and Convex Analysis.
- Classical methods. Direct methods.
- Control theory. Controllability. Optimal control.
- Minimal time linear autonomous problems: existence of an optimal control and extremal controls; normality and uniqueness of the optimal control.
- Prerequisites of Functional Analysis and Convex Analysis.
- Classical methods. Direct methods.
- Control theory. Controllability. Optimal control.
- Minimal time linear autonomous problems: existence of an optimal control and extremal controls; normality and uniqueness of the optimal control.
Teaching Methods
Structured exposition, examples with emphasis on applications and on solving exercises.
To stimulate students' initiative, so that classes become essentially centered on students' activities, guided by their teacher; instead of on teacher's activities, copied by students. Particularly in what concerns submission of questions and / or suggestions of application and / or description of contents, the solving of exercises, participation in discussions, etc.
To stimulate students' initiative, so that classes become essentially centered on students' activities, guided by their teacher; instead of on teacher's activities, copied by students. Particularly in what concerns submission of questions and / or suggestions of application and / or description of contents, the solving of exercises, participation in discussions, etc.
Assessment
- Continuous evaluation - two tests with equal weight in the final result (50%) or one written test and one written work elaborated by the student both with equal weight in the final result (50%). A minimum classification of 8 marks is required in each test/work to obtain approval;
or
- Exam regime - one exam with a weight of 100% in the final result.
or
- Exam regime - one exam with a weight of 100% in the final result.
Teaching Staff
- Luís Manuel Balsa Bicho [responsible]
Certificações
