470-8742/01 – Methods of Optimization (MONT)
| Gurantor department | Department of Applied Mathematics | Credits | 3 |
| Subject guarantor | doc. Ing. Petr Beremlijski, Ph.D. | Subject version guarantor | doc. Ing. Petr Beremlijski, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | |
| Intended for the faculties | FMT, USP | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The student will be able to recognize basic classes of optimization problems and will understand conditions of their solvability and correct formulation. Effective algorithms, heuristics and software will be presented in an extent that is useful for solving engineering problems, so that the student will be able to apply their knowledge to the solution of practical problems.
Teaching methods
Lectures
Tutorials
Summary
Optimization methods are basic tools for improving design and technology. The students will learn about basic optimization problems, conditions of their solvability and correct formulation. Effective algorithms, heuristics and software will be presented in an extent that is useful for the soluving engineering problems.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Verification of study:
Written exam (max 10 marks).
Project (max 20 marks)
Conditions for credit:
Minimum 10 marks on tests and project.
E-learning
Other requirements
Additional requirements for students are not.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
Unconstrained minimization. One-dimensional minimization of unimodular functions.
Conditions of minimum, the Newton method and its modification. Gradient methods.
Constrained minimization. Karush-Kuhn-Tucker conditions of optimality.
Penalization methods for constrained minimization. Augmented Lagrangians
Duality in convex programming. Saddle points.
Non-smooth optimization, subgradients and optimality conditions.
Software.
Exercises:
Introduction to the MATLAB programming.
Implementation of the golden section and Fibonacci series methods.
Implemenation of the Newton-like methods.
Implementation of the gradient based method.
Implementation of the penalty methody for equality constrained minimization.
Implementation of the augmented Lagrangian metod.
Solution of selected engeneering problems using optimization software.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction