Nonlinear Programming

Garant předmětu:

Lecturer:

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:

Basic course of Calculus and Linear Algebra.

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:

Knowledge:

Mathematical basis of nonlinear optimization.

Abilities:

Use of nonlinear optimization algorithms in practice.

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:

http://mmg.fjfi.cvut.cz/~fucik/index.php?page=01NELI

No time-table has been prepared for this course

The course is a part of the following study plans:

• Matematické inženýrství (compulsory course of the specialization)
• Aplikace softwarového inženýrství (elective course)