Nonlinear Optimization

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:

Exam: 2 questions selected from 9 areas of questions listed on the course website https://mmg.fjfi.cvut.cz/~fucik/index.php?page=01NELO

Syllabus of lectures:

1. General optimization problem: overview of basic optimization problems, summary of necessary mathematical apparatus

2. Convex sets and functions, basic properties and examples, operations preserving convexity, separability, quasi-convex and pseudoconvex functions

3. Lagrange duality, strong and weak duality

4. Optimality conditions for optimization problems without constraints

5. Optimality conditions for optimization problems with constraints

6. Black-box optimization

7. Algorithms for problems without constraints: gradient methods, quasi-Newton methods, least squares method

8. Algorithms for constrained problems: overview of basic interior and exterior point methods

9. Examples of implementation of unconstrained optimization problems

10. Examples of implementation of constrained optimization problems

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:

No time-table has been prepared for this course

The course is a part of the following study plans: