Course: Nonlinear Programming

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Course title Nonlinear Programming
Course code KMA/NLP
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech, English
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • Netuka Horymír, RNDr. Ph.D.
  • Pastor Karel, doc. Mgr. Ph.D.
  • Burkotová Jana, Mgr. Ph.D.
Course content
1. Constrained optimization, its importance for applications, examples. Introductory definitions and basic conceptions. 2. First-order necessary optimality conditions. Karush-Kuhn-Tucker conditions. Geometric interpretation of KKT conditions. 3. First-order optimality conditions for minimization on convex sets. Sufficient optimality conditions for problems of this type. 4. Constraint qualifications in nonlinear programming problems. Useful constraint qualifications conditions. 5. Lagrangian function. Second-order necessary optimality conditions. Second-order sufficient optimality conditions. 6. Saddle points of Lagrangian function and their connection with optimization problems. Lagrangian dual problems and their properties. 7. Complementarity problems and their relation to nonlinear programming. Linear complementarity problem. Lemke's method. 8. Quadratic programming and its importance. Methods for solution of problems with equality constraints. 9. Active set method for convex quadratic programming problems having inequality constraints. 10. Methods for nonlinear programming problems with linear constraints - null-space method and gradient projection method. 11. Penalty methods for general nonlinear programming. Quadratic penalty function, barrier functions. Augmented Lagrangian method. 12. Principles of sequential quadratic programming method. Concept of interior-point methods.

Learning activities and teaching methods
Lecture, Monologic Lecture(Interpretation, Training), Demonstration
  • Attendace - 52 hours per semester
  • Homework for Teaching - 25 hours per semester
  • Preparation for the Exam - 45 hours per semester
Learning outcomes
Gain knowledge about theory and algorithms required to solve nonlinear programming problems.
Knowledge Gain useful knowledge about theory and algorithms in order to study and solve nonlinear programs.
Student has to pass the course Numerical methods of optimization. Standard knowledge from mathematical analysis and linear algebra. Information concerning numerical methods are welcomed, but not necessary. Elemental experience with computation on PC.

Assessment methods and criteria
Oral exam, Seminar Work

Credit: the student has to compute given examples. Exam: the student has to understand the subject and be acquainted with theoretical and practical aspects of the methods.
Recommended literature
  • D.G. Luenberger, Y. Ye. (2008). Linear And Nonlinear Programming. 3rd Edition.
  • J. Machalová, H. Netuka. (2013). Nelineární programování: Teorie a metody. Olomouc.
  • J. Nocedal, S. J. Wright. (1999). Numerical Optimization. Springer.
  • K.G. Murty. (1988). Linear Complementarity, Linear and Nonlinear Programming. Berlin.
  • M.S. Bazaraa, H.D. Sherali, C.M. Shetty. (2006). Nonlinear Programming. Theory And Algorithms. 3rd Edition.
  • O. Došlý. (2005). Základy konvexní analýzy a optimalizace v R^n. Brno.
  • S. Míka. (1997). Matematická optimalizace. FAV ZČU, Plzeň.
  • Z. Dostál, P. Beremlijski. (2012). Metody optimalizace. Ostrava.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 2 Winter
Faculty of Science Applications of Mathematics in Economy (2015) Mathematics courses 2 Winter
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Winter