Topics in Numerical Optimization

BEA514 Topics in Numerical Optimization

  • Topics


    Topics will be lectured in the following sequence:

    • General overview: Difference- and differential equations and stability analysis
    • General overview: Dynamic Optimal Control (OC)
    • Labs on first order conditions (FOC) and open loop policies (in Matlab)
    • Dynamic programming (DP) and the Hamilton-Jacobi-Bellman (HJB) equation. A general discretization scheme for the HJB.
    • Infinite horizon stochastic optimization and the numerical probability approach.
    • Alternative numerical approaches

  • Learning outcome

    Learning outcome

    After completion of the course, the candidate should be able to:


    • critically read and comprehend relevant scientific papers addressing dynamic optimization
    • formulate models and propose numerically solution procedures to dynamic challenges in economics and management science using the tools from optimal control theory
    • constructively approach deterministic and stochastic dynamic decision problems (not only limited to linear or linear-quadratic problems).
    • recognize numerical schemes producing decision variables (policies) in feedback form and their applicability.


    The candidates should be able to

    • formulate and model operational management tasks and assign feasible numerical solution schemes
    • analyze and evaluate potential nonlinear and dynamic and stochastic effects on economic quantities and resources and how they may depending on policy choices
    • design a probability based discretization approach to Hamilton-Jacobi-Bellman (HJB) formulated dynamic decision problems to determine the value functions and optimal feedback policies for such projects


    General competence

    • manage complex interdisciplinary research projects involving optimal time-based decisions tasks in an operational setting
    • recognize the potential as well as the limitations of modern numerical solution approaches in the field, particularly the-curse-of-dimensionality and potential workarounds
    • communicate and bridge the gap between theoretical economic modeling and feasible real world approaches

  • Required prerequisites

    Required prerequisites

    Knowledge of medium advanced calculus and some familiarity with differential equations and stability analysis and introductory probability theory and vector algebra.

  • Requirements for course approval

    Requirements for course approval

    • Activity in class. 

  • Assessment


    1. Two assignments.
    2. Short oral examination at the end of the course.

  • Grading Scale

    Grading Scale

    Pass / Fail

  • Computer tools

    Computer tools

    The use of high-level programing in Maple and MatLab will be an integrated part of the course.

  • Semester



  • Literature


    All topics in the course are covered by scientific papers and selected parts in advanced

    textbooks such as

    -H. J. Kushner and Paul Dupois, Numerical Methods for Stochastic Control

    Problem in Continuous Time, Springer, 2001, and

    -D. Bertsekas, Dynamical Programming in Deterministic and Stochastic Models,

    Prentice-Hall, NJ, 1987.

    The course material is given as handouts and web links.


ECTS Credits
Teaching language

Course responsible

Professor Leif Sandal , Department of Business and Management Science