Optimal Programming II

  • Credits: 6
  • Ending: Examination
  • Range: 2P + 2C
  • Semester: summer
  • Year: 2
  • Faculty of Economic Informatics

Teachers

Included in study programs

Data Science in Economics

Teaching results

In particular, students acquire the following abilities:
- to formulate nonlinear optimization models
- to identify problems associated with solving nonlinear problems
- to select algorithm for solving nonlinear programming problems.
Students acquire in particular the following skills:
- to model decision-making problems at the microeconomic and macroeconomic level on the basis of nonlinear optimization models.
- to analyze of nonlinear problems, solution through Python software system.
Students will acquire the following competencies:
- practical skills and competencies with the application of optimization methods with nonlinear constraints, their analysis and solution using appropriate software (Python language)

Indicative content

1. Nonlinear optimization models in economic decision making, applications of nonlinear models
2. General formulation of nonlinear programming problems, classification of algorithms for solving such problems, complexity of algorithms
3. Software systems for solving nonlinear programming problems (Python and Gams language)
4. Convex analysis.
5. Optimality conditions in nonlinear programming problems, Kuhn-Tucker optimality conditions
6. Lagrange function and duality theory
7. Methods for solving unconstrained problems, scalar function of one variable, scalar function of more than one variables, Python software system
8. Methods for solving constrained problems (Langrange's method, penalty and barrier functions)
9. Separable programming and fractional programming
10. Quadratic programming.
11. Methods for solving constrained problems, Python software system
12. Evolutionary algorithms, solving unconstrained problems
13. Evolutionary algorithms, solving constrained problems

Support literature

Fendek, M.: Nelineárne optimalizačné modely a metódy, Ekonóm, Bratislava 1998
Alt, W.: Nichtlineare Optimierung. Eine Einführung in Theorie, Verfahren und Anwendungen. Vieweg Verlag. Berlin 2002.
Avriel, M.: Nonlinear Programming. Analysis and Methods. Doverr Publications. New York 2003
Bazaraa, M. - C. M. Shetty, C.M.: Nonlinear Programming: Theory and Algorithms. Wiley-Interscience. New York 2006
Bonnans, J. F. - Gilbert, J. C. – Lemarechal, C.: Numerical Optimization. Springer Verlag, Berlin 2003.

Requirements to complete the course

40 % final paper and continuous testing
60 % final exam

Student workload

Total study load (in hours): 6 credits x 26 hours = 156 hours
Lectures participation: 26 hours
Seminars participation: 26 hours
Final paper preparation: 52 hours
Preparation for the exam and continuous tests: 52 hours

Language whose command is required to complete the course

Slovak

Date of approval: 10.02.2023

Date of the latest change: 16.05.2022