2024
Dynamic Optimization
Name: Dynamic Optimization
Code: MAT13506L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
The objective of this course is the basic training in theory of optimization of dynamic systems, with a view to the future development, either of the knowledge in this area, as well as its use in other areas of Mathematics or Economics and Management.
At the end of u.c. It is intended that the student learns:
- formulate optimal control models and dynamic programming in various contexts in the areas of Economics, Management, Engineering, Biology;
- know the main methods of solving these problems.
In addition, it is intended to develop:
- students' abstract thinking to solve, more simply and more generally, concrete problems
- capacity for abstraction, creative intuition, model building and critical thinking.
At the end of u.c. It is intended that the student learns:
- formulate optimal control models and dynamic programming in various contexts in the areas of Economics, Management, Engineering, Biology;
- know the main methods of solving these problems.
In addition, it is intended to develop:
- students' abstract thinking to solve, more simply and more generally, concrete problems
- capacity for abstraction, creative intuition, model building and critical thinking.
Contents
Optimization of dynamic systems and processes, control problems. Historical introduction.
Calculation of variations. Important particular examples: geodetic, brachistochrone problem, revolution surfaces of minimal area. Euler's equation. Condition of transversality.
Control theory. Controllability. Optimal control problems. Examples in Economics and Management. Pontryagin's maximum principle. Model of optimal economic growth. Control problem in discrete time.
Dynamic programming. Multistage decision processes. Bellman's principle of optimality. Typical problems of dynamic programming.
Calculation of variations. Important particular examples: geodetic, brachistochrone problem, revolution surfaces of minimal area. Euler's equation. Condition of transversality.
Control theory. Controllability. Optimal control problems. Examples in Economics and Management. Pontryagin's maximum principle. Model of optimal economic growth. Control problem in discrete time.
Dynamic programming. Multistage decision processes. Bellman's principle of optimality. Typical problems of dynamic programming.
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.
Assessment
Knowledge assessment comprises two alternative aspects: continuous assessment and assessment by exam. The continuous assessment consists of two frequencies (the final grade is the arithmetic average of the two frequencies, each one with a minimum grade of 8 points), carried out during the period. Assessment by exam consists of a global exam, which will be carried out in the normal period and/or in the appeal period.
Teaching Staff
- Luís Miguel Zorro Bandeira [responsible]
Certificações
