Code: 01NELO Nonlinear Optimization
Lecturer: doc. Ing. Radek Fučík Ph.D. Weekly load: 3P+0C Completion: EX
Department: 14101 Credits: 4 Semester: S
Description:
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.
Contents:
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
Recommended literature:
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.
Keywords:
Nonlinear optimization, convex sets, convex functions, Lagrange duality, Karush-Kuhn-Tuckerovy conditions, unconstrained optimization, optimization with constraints.

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