Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


The students learn 
1. the basic notions and classes of dynamic optimization problems, 
2. to build and solve dynamic optimization models.

Credits: 5

Schedule: 24.02.2022 - 24.02.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Ahti Salo, Nuutti Hyvönen

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English


  • valid for whole curriculum period:

    Optimization methods for dynamic systems: dynamic programming, calculus of variations, maximum principle, numerical solution methods. Application examples on engineering, economics and biology.


Study Material
  • valid for whole curriculum period:

    D.E. Kirk: Optimal Control Theory; M.I. Kamien, N.L. Schwarz: Dynamic Optimization - the Calculus of Variations and Optimal Control in Economics and Management; D.P. Bertsekas: Dynamic Programming and Optimal Control, vols I and II; lecture notes

Substitutes for Courses


Further Information
  • valid for whole curriculum period:

    Teaching Period:

    2020-2021 Spring III

    2021-2022 Spring III

    Course Homepage:

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu ( instead of WebOodi.