|David Hartman||Charles University
Nonlinear Optimisation Algorithms
This site contains the description of the course Nonlinear Optimisation Algorithms (NOPT008) organized primarily for students of the Master's Computer Science program in Czech as well as English versions. This course is one of the Suggested Elective courses (Povinně volitelné in Czech) for specialization Optimization, see description in Czech or English. This course follows the previous one called Fundamentals of Nonlinear Optimization (NOPT018), which discusses the theoretical formulations of a nonlinear optimization problem and their properties.
Many real-world tasks are optimization in nature. The classic solution to such problems consists of the use of linear programming. In many cases, however, such a definition is imprecise, and even approximation techniques are not providing satisfactory results. In these cases, we usually adopt techniques of nonlinear programming. These techniques assume more complex structures of conditions and/or optimization functions.
In the entire nonlinear optimization task, several vital steps affect its success. In addition to the clever definition of the optimization problem, in terms of precision and computational complexity, another crucial aspect is using suitable optimization algorithms. Due to the more complex structure, algorithms in this area are typically iterative with decreasing estimation error and only sometimes guarantee convergence to the global optimum. This course deals not only with the construction of the methods but also their speed and convergence.
The course consists of the following topics.
The course is organized in lectures providing basic theory on topics given above. Seminars are based on solution of individual project.
Continuous evaluation is based on the result of individual project. Final evaluation consists of combined written and oral exam.
This section contains the list of references basic and advanced for the course, some of which are available online..
|Stephen Boyd and Lieven Vandenberghe||Jorge Nocedal and Stephen Wright||Andrzej Ruszczynski|
|Convex Optimization||Numerical Optimization||Nonlinear Optimization|
|Cambridge University Press, 2004||Springer, 2006||Princeton University Press, 2006|
Relevant lecture notes
|Milan Hladík||Ladislav Lukšan|
|Základy Nelineární Optimalizace||Numerické optimalizačnı́ metody|
|Milan Hladík Press, 2021||The Institute of Computer Science (CAS), 2017|