KMA/NLP Nonlinear Programming

Lecturer: Horymír Netuka
Lecture: 3 hours/week + exercise 1 hour/week
Credits: 4
Winter semester
Form of course completion: course credit, exam

• Constrained optimization, its importance for applications, examples. Introductory definitions and basic conceptions.
• First-order necessary optimality conditions. Karush-Kuhn-Tucker conditions. Geometric interpretation of KKT conditions.
• First-order optimality conditions for minimization on convex sets. Sufficient optimality conditions for problems of this type.
• Constraint qualifications in nonlinear programming problems. Useful constraint qualifications conditions.
• Lagrangian function. Second-order necessary optimality conditions. Second-order sufficient optimality conditions.
• Saddle points of Lagrangian function and their connection with optimization problems. Lagrangian dual problems and their properties.
• Complementarity problems and their relation to nonlinear programming. Linear complementarity problem. Lemke's method.
• Quadratic programming and its importance. Methods for solution of problems with equality constraints.
• Active set method for convex quadratic programming problems having inequality constraints.
• Methods for nonlinear programming problems with linear constraints - null-space method and gradient projection method.
• Penalty methods for general nonlinear programming. Quadratic penalty function, barrier functions. Augmented Lagrangian method.
• Principles of sequential quadratic programming method. Concept of interior-point methods.