Nonlinear Optimization

Code	Completion	Credits	Range
01NELO	ZK	4	3P+0C

Course guarantor:

Radek Fučík

Lecturer:

Radek Fučík

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Nonlinear optimization problems find their application in may areas of applied mathematics. The lecture covers the

basics of mathematical programming theory with emphasis on convex optimization and basic methods for unconstrained

and constrained optimization. The lecture is supplemented by illustrative examples.

Requirements:

Course of linear algebra, topology, mathematical analysis of functions of several variables, basic programming and algorithmization

Syllabus of lectures:

1. Mathematical programming: introduction, overview of basic optimization problems, linear and nonlinear

programming, weak and strong Lagrange duality,

2. Summary of the required mathematical apparatus: pseudo-inverse matrix, least squares method, conjugate gradient

method

3. Convex sets and functions, basic properties and examples, operations preserving convexity

4. Unconstrained optimization problems

5. Constrained optimization tasks

6. Algorithms unconstrained optimization problems

7. Algorithms constrained optimization tasks: overview of basic methods, penalty methods, inner point methods,

logarithmic barrier function

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] Bertsekas, Dimitri P., and Athena Scientific. Convex optimization algorithms. Belmont: Athena Scientific, 2015.

[2] Nesterov, Yurii. Lectures on convex optimization. Vol. 137. Springer, 2018.

[3] Jeter, Melvyn. Mathematical programming: an introduction to optimization. Routledge, 2018.

Recommended references:

[3] Stephen Boyd and Lieven Vandenberghe, Convex optimization, Cambridge University Press 2004

[4] Li, Li. Selected Applications of Convex Optimization. Vol. 103. Springer, 2015.

Note:

Further information:

https://mmg.fjfi.cvut.cz/~fucik/index.php?page=01NELO

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: