Course: Nonlinear Programming

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Course title Nonlinear Programming
Course code KMA/NLPA
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Netuka Horymír, RNDr. 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. Generalizations of convexity. First-order sufficient optimality conditions for constrained optimization. 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. 12. Augmented Lagrangian method. 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 - 40 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.
Prerequisites
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.
KMA/NMO

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
  • 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. Helderman-Verlag Berlin.
  • R. Fletcher. (1991). Practical methods of optimization. John Wiley & Sons.
  • S. Míka. (1997). Matematická optimalizace. FAV ZČU, Plzeň.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester