457-0313/02 – Methods of Optimization (MO)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | prof. RNDr. Zdeněk Dostál, DSc. | Subject version guarantor | prof. RNDr. Zdeněk Dostál, DSc. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | 2 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2003/2004 | Year of cancellation | 2009/2010 |
| Intended for the faculties | FEI | 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
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:
Way of continuous check of knowledge in the course of semester
Verification of study:
Written exam on unconstrained optimization (45 minutes, max 10 marks).
Written exam on constrained optimization (45 minutes, max 10 marks).
Conditions for credit:
At least 25 marks on progress assessment and projects.
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
An introduction to the calculus of variations. Linear spaces, funkcionls and their differentials (Fréchet, Gateaux).
Euler equation and the solution of the classical problems of variational calculus.
Unconstrained minimization. One-dimensional minimization of unimodular functions.
Conditions of minimum, the Newton method and its modification. Gradient methods, method of conjugate gradients.
Constrained minimization. Karush-Kuhn-Tucker conditions of optimality.
Penalization and barrier methods for constrained minimization. Feasible direction method (SLP) and active set strategy for bound constrained problems.
Duality in convex programming. Saddle points, Uzawa algorithm and augmented Lagrangians.
Linear programming, simplex method.
Non-smooth optimization, subgradients and optimality conditions.
Global optimization, genetic and evolutionary algorithms, simulated annealing, tabu search.
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 conjugate gradient method.
Implementation of the penalty methody for equality constrained minimization.
Implementation of the feasible direction method (SLP).
Implementation of the active set method for bound constrained quadratic programming.
Implementation of the augmented Lagrangian metod.
Implementation of algorithms for global optimization.
Solution of selected engeneering problems using optimization software.
Projects:
Comparing performance of the methods for unconstrained optimization using a numerical example (max 10 marks).
Comparing performance of the methods for constrained optimization using a numerical example (max 10 marks).
Solution of a selected engineering problem (max 10 marks).
Computer labs:
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 conjugate gradient method.
Implementation of the penalty methody for equality constrained minimization.
Implementation of the feasible direction method (SLP).
Implementation of the active set method for bound constrained quadratic programming.
Implementation of the augmented Lagrangian metod.
Implementation of algorithms for global optimization.
Solution of selected engeneering problems using optimization software.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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