A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.
MI-LOM.16 Linear Optimization and Methods Extent of teaching: 2P+1C Instructor: Completion: Z,ZK Department: 18101 Credits: 5 Semester: Z Annotation:
Students learn the applications of optimization methods in computer science, economics, and industry. They are aware of practical importance of linear and integer programming. They are able to work with optimization software and are familiar with languages used in programming of that software. They get skills in formalization of optimization problems in computer science (such as scheduling of tasks to processors, analysis of network flows), distribution and allocation of resources (transportation problems, travelling salesman problems, etc.), issues from economics, and modelling of conflicts via the game theory. They get an overview of computational complexity of optimization problems. They get orientation in algorithms in linear programming.
Lecture syllabus:
1. Classification of optimization techniques: linear and integer programming, nonlinear optimization, continuous optimization, special forms of linear programs, general convex programming, multicriteria optimization. 2. Mathematical formulation of optimization problems (optimization and combinatorics, distribution, allocation, network, statistical problems, etc.). 3. Models of conflicting situations, introduction to the game theory. 4. Linear algebra: matrices and linear mappings, eigenvalues and eigenvectors, basic bounds, positive (semi)definiteness, $L_k$-norms, matrix norms. 5. Fundamentals of theory of linear and integer programming and their geometry, forms of linear programs. 6. The simplex algorithm. 7. Duality in linear programming. 8. Applications of duality in combinatorics and algorithmic design. 9. Classifications of optimization problems using the complexity theory. 10. The ellipsoid algorithm. 11. Interior point algorithms. 12. Algorithms for integer programming. 13. Implementation issues (numerical stability, sparse matrices, approximate and exact solutions, date structures). Seminar syllabus:
1. Formulation of optimization problems. 2. Formulation of optimization problems --- continued. 3. Syntax of optimization languages: LINGO. 4. Solution of particular problems in v LINGO. 5. Syntax of optimization languages: CPLEX. 6. Solution of particular problems in CPLEX. 7. Syntax of optimization languages: MatLab. 8. Solution of particular problems in MatLab. 9. Sensitivity; applications of duality. 10. The Simplex Algorithm. 11. Complexity of the Simplex Algorithm; average and exponential case. 12. Multicriteria problems reducible to linear programming I. 13. Multicriteria problems reducible to linear programming II. Literature:
1. Cook, W. J., Cunningham, W. H., Pulleyblank, W. R., Schrijver, A. ''Combinatorial Optimization''. Wiley-Interscience, 1997. ISBN 047155894X. 2. Chvatal, V. ''Linear Programming''. W. H. Freeman, 1983. ISBN 0716715872. 3. Matousek, J., Gärtner, B. ''Understanding and Using Linear Programming''. Springer, 2006. ISBN 3540306978. 4. Roos, C., Terlaky, T., Vial, J. P. ''Interior Point Methods for Linear Optimization''. Springer, 2005. ISBN 0387263780. 5. Schrijver, A. ''Theory of Linear and Integer Programming''. Wiley, 1998. ISBN 0471982326. 6. Thie, P. R., Keough, G. E. ''An Introduction to Linear Programming and Game Theory''. Wiley-Interscience, 2008. ISBN 0470232862. 7. Venkataraman, P. ''Applied Optimization with MATLAB Programming''. Wiley, 2009. ISBN 047008488X. Requirements:
Informace o předmětu a výukové materiály naleznete na http://mi-lom.polyedr.cz/ The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester NI-TI.2018 Computer Science V 1,3 MI-ZI.2016 Knowledge Engineering V Není MI-ZI.2018 Knowledge Engineering V Není MI-SP-TI.2016 System Programming V Není MI-SP-SP.2016 System Programming V Není MI-SPOL.2016 Unspecified Branch/Specialisation of Study V Není MI-WSI-WI.2016 Web and Software Engineering V Není MI-WSI-SI.2016 Web and Software Engineering V Není MI-WSI-ISM.2016 Web and Software Engineering V Není MI-NPVS.2016 Design and Programming of Embedded Systems V Není MI-PSS.2016 Computer Systems and Networks V Není MI-PB.2016 Computer Security V Není
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