Syllabus
1. Optimization problems and their formulations. Applications in economy and in mathematical statistics.
2. Selected parts of convex analyses (convex sets, convex cones, extreme points, extreme directions).
3. Selected parts of functional theory. Differentiation in Peano sense. Convex functions with several variables (epigraph, subgradient, subdiferential).
4. Separation theorems (Farkas theorem).
5. Theory of linear programming (structure of the set of all feasible solutions, basic theorem of linear programming, duality).
6. Direct method for solving linear programming, simplex method, dual simplex method, postoptimization.
7. Theory of nonlinear programming (saddle point condition, Karush-Kuhn-Tucker optimality conditions, constraint qualifications).
8. Symmetric nonlinear programming.
9. Linear and convex programming as a particular case of nonlinear programming.
10. Transport problem as a particular case of linear programming.
11. Main ideas of algorithms for nonlinear programming.
12. Matrix games and linear programming, minimax theorem.
Annotation
Optimization in economy and in mathematical statistics.
Basis of convex analysis.
Theory of linear and nonlinear programming.
Symmetric nonlinear programming.
Supposed knowledge:
Linear algebra, functional analysis (functions with several arguments, constraint extrema problems).