Syllabus
1. Optimization problems and their formulations.
2. Selected parts of convex analyses (convex cones, convex function, epigraph, subdifferential).
3. Separation theorems (Farkas theorem).
4. Theory of nonlinear programming. (Karush-Kuhn-Tucker optimality condition, constraints qualifications).
5. Linear a convex programming like a particular case of nonlinear programming.
6. Symmetric problem of nonlinear programming.
Annotation
Optimization in economy and statistics, convex analysis, introduction to non-linear programming, theory of linear programming with respect to convex analysis and general optimization.
Supposed knowledge: Mathematical analysis (functions with several arguments, constraint extrema problems).