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: 13.01.2021 - 25.02.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Harri Ehtamo

Teacher in charge (applies in this implementation): Harri Ehtamo

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

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    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 01.08.2020-31.07.2022:

    Exam. Bonus points from home work and exercise sessions

  • Applies in this implementation:

    30 points from exam. A maximum of 12 extra points can be obtained from homework (12 points)
    and activity on Slack discussion forum (6 points). For example,  6
    points from homework and 6 from activity, or 12 points from homework,
    and 0 from activity.  Grade/gradelimit:






    To pass the course one must get at least 12 points in the exam.

  • Valid 01.08.2020-31.07.2022:

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

  • Applies in this implementation:

    No contact hours. The course is a self-study course.


Study Material
  • Valid 01.08.2020-31.07.2022:

    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
  • Valid 01.08.2020-31.07.2022:

    Mat-2.3148 Dynamic optimization

  • Valid 01.08.2020-31.07.2022:

    MS-A00XX Matrix Algebra, MS-A01XX Differential and integral calculus 1, and MS-A01XX Differential and integral calculus 2.