CTU FEE Moodle
Optimization
Optimization B0B33OPT
| Credits | 7 |
| Semesters | Both |
| Completion | Assessment + Examination |
| Language of teaching | Czech |
| Extent of teaching | 4P+2C |
Annotation
The course provides an introduction to mathematical optimization, specifically to optimization in real vector spaces of finite dimension. The theory is illustrated with a number of examples. You will refresh and extend many topics that you know from linear algebra and calculus courses.
Study targets
The aim of the course is to teach students to recognize optimization problems around them, formulate them mathematically, estimate their level of difficulty, and solve easier problems.
Course outlines
1. General problem of continuous optimization.
2. Over-determined linear systems, method of least squares.
3. Minimization of quadratic functions.
4. Using SVD in optimization.
5. Algorithms for free local extrema (gradient, Newton, Gauss-Newton, Levenberg-Marquardt methods).
6. Linear programming.
7. Simplex method.
8. Convex sets and polyhedra. Convex functions.
9. Intro to convex optimization.
10. Lagrange formalism, KKT conditions.
11. Lagrange duality. Duality in linear programming.
12. Examples of non-convex problems.
13. Intro to multicriteria optimization.
2. Over-determined linear systems, method of least squares.
3. Minimization of quadratic functions.
4. Using SVD in optimization.
5. Algorithms for free local extrema (gradient, Newton, Gauss-Newton, Levenberg-Marquardt methods).
6. Linear programming.
7. Simplex method.
8. Convex sets and polyhedra. Convex functions.
9. Intro to convex optimization.
10. Lagrange formalism, KKT conditions.
11. Lagrange duality. Duality in linear programming.
12. Examples of non-convex problems.
13. Intro to multicriteria optimization.
Exercises outlines
At seminars, students exercise the theory by solving problems together using blackboard and solve optimization problems in Matlab as homeworks.
Literature
Basic:
Online lecture notes Tomáš Werner: Optimalizace (see www pages of the course).
Optionally, selected parts from the books:
Lieven Vandenberghe, Stephen P. Boyd: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares, Cambridge University Press, 2018.
Stephen Boyd and Lieven Vandenberghe: Convex Optimization, Cambridge University Press, 2004.
Online lecture notes Tomáš Werner: Optimalizace (see www pages of the course).
Optionally, selected parts from the books:
Lieven Vandenberghe, Stephen P. Boyd: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares, Cambridge University Press, 2018.
Stephen Boyd and Lieven Vandenberghe: Convex Optimization, Cambridge University Press, 2004.
Requirements
Linear algebra. Calculus, including intro to multivariate calculus. Recommended are numerical algorithms and probability and statistics.
Responsible for the data validity:
Study Information System (KOS)