Syllabus
1. Convex and affine sets, their properties
2. Convex functions, their properties, quasiconvex functions
3. Convex optimization problems, convex optimization, linear optimization, quadratic optimization, geometric programming, vector optimization
4. Duality, Lagrange dual function, Lagrange dual problem, geometric interpretation, perturbation and sensitivity analysis
5. Applications in approximation and data processing
6. Geometric applications, Support Vector Machines
7. Statistical applications (maximum likelihood method, MAP)
8. Algorithms for minimization without constraints or with constraints in the form of equalities
9. Interior point methods
Annotation
Compulsory course for the programme Mathematics for Information Technologies.