Nonlinear Continuous Optimization and Numerical Methods
Code  Completion  Credits  Range  Language 

MINON.16  Z,ZK  5  2P+1C  Czech 
 Course guarantor:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Theoretical Computer Science
 Synopsis:

Students will be introduced to nonlinear continuous optimization, principles of the most popular methods of optimization and applications of such methods to realworld problems. They will also learn the finite element method and the finite difference method used for solving ordinary and partial differential equations in engineering. They will learn to solve systems of linear algebraic equations that arise from discretization of the continuous problems by direct and iterative algorithms. They will also learn to implement these algorithms sequentially as well as in parallel.
 Requirements:

Basic knowledge of linear algebra (vectors, matrices, systems of linear algebraic equations, Gaussian elimination method), polynoms, differential calculus (derivative, integral).
 Syllabus of lectures:

1. Partial derivative, gradient, hessian.
2. Continuous optimization of the 1st and 2nd order.
3. QuasiNewton method, conjugate gradient method.
4. Application of methods of nonlinear continuous optimization.
5. Introduction to ordinary and partial differential equations (taxonomy, the notion of the solution, physical interpretation).
6. Ordinary differential equations  boundary value problem (exact solution, finite difference method, finite differences).
7. Ordinary differential equations  boundary value problem (finite element method).
8. Partial differential equations  stationary cases (finite difference method).
9. Partial differential equations  stationary cases (finite element method).
10. Ordinary differential equations  initial value problem.
11. Partial differential equations  nonstationary problems.
12. Iterative methods (GaussSeidel method, conjugate gradient method).
13. Introduction to domain decomposition methods. Parallel solvers of sets of linear equations.
 Syllabus of tutorials:
 Study Objective:

The module gives an introduction to continuous optimization with respect to the solution of complicated problems, e.g., data approximation or identification of model parameters. The second part deals with several parts of computational sciences, with the emphasis on the finite element method and the finite difference method which are massively used in all engineering branches, not only in academic community but also in industry.
 Study materials:

1. Kruis, J. ''Domain Decomposition Methods for Distributed Computing''. SaxeCoburg Publications, 2007. ISBN 1874672237.
2. Petzold, L. R. ''Computer Methods for Ordinary Differential Equations and DifferentialAlgebraic Equations''. Society for Industrial and Applied Mathematics, 1998. ISBN 0898714125.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Master branch System Programming, spec. Computer Science, in Czech, 20162017 (compulsory course of the branch)
 Master specialization Computer Science, in Czech, 20182019 (PS)