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: 12.01.2022 - 24.02.2022

Teacher in charge (valid for whole curriculum period):

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

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.

Assessment Methods and Criteria
  • valid for whole curriculum period:

    Exam. Bonus points from home work and exercise sessions

  • valid for whole curriculum period:

    Contact hours 48 h. Attendance is not compulsory.
    Voluntary home exercises 15h 
    Autonomous studies 65h


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.