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Large-scale optimization: Exact methods - NOPT059

Title:	Optimalizace velkých problémů: přesné metody
Guaranteed by:	Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2025
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Additional information:	https://jbulin.github.io/teaching/spring/nopt059/

Guarantor:	RNDr. Jakub Bulín, Ph.D. RNDr. Jiří Fink, Ph.D. Mgr. Marika Ivanová, Ph.D.
Class:	Informatika Mgr. - Teoretická informatika Informatika Mgr. - Diskrétní modely a algoritmy
Classification:	Informatics > Informatics, Software Applications, Computer Graphics and Geometry, Database Systems, Didactics of Informatics, Discrete Mathematics, External Subjects, General Subjects, Computer and Formal Linguistics, Optimalization, Programming, Software Engineering, Theoretical Computer Science, Optimalization

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Annotation -

Advanced lecture on exact optimization algorithms based on Linear Programming and Convex Optimization for solving real-life problems.

Last update: Hric Jan, RNDr. (12.05.2022)

Aim of the course -

Understand the main principles of various exact optimization methods based on linear programming and combinatorial optimization with emphasis on large-scale instances. Learn how to apply these methods in practice. (The course is suitable for 3rd-year bachelor's students and for master's students.)

Last update: Bulín Jakub, RNDr., Ph.D. (06.05.2024)

Course completion requirements -

Students are expected to implement practical homework assignments and pass theoretical examination. The nature of homework assignments excludes the possibility of repeated attempts to get credit.

Last update: Bulín Jakub, RNDr., Ph.D. (13.05.2022)

Literature -

Wolsey, Laurence A. Integer programming. Vol. 42. New York: Wiley, 1998.

Cunningham, Cook, Pulleyblank, Schrijver. Combinatorial optimization, John Wiley & Sons, 1997

Kochenderfer, Mykel J., and Tim A. Wheeler. Algorithms for optimization. MIT Press, 2019.

Desaulniers, Guy, Jacques Desrosiers, and Marius M. Solomon, eds. Column generation. Vol. 5. Springer Science & Business Media, 2006.

Last update: Bulín Jakub, RNDr., Ph.D. (13.05.2022)

Syllabus -

Linear programming, duality, complementary slackness

Integer linear programming, Branch and bound

Gomory-Chvátal cutting plane, lazy constraint

Column generation, Dantzig-Wolve decomposition

Lagrangian relaxation

Applications, e.g. Cutting Stock Problem, Vehicle Routing Problems, Job Scheduling

Knowledge of the basics of linear programming and duality will be expected, recommended prerequisite: Linear Programming and Combinatorial Optimization (NOPT048).

The course is taught bi-yearly, alternating with the course Large-scale optimization: Metaheuristics (NOPT061).

Last update: Fink Jiří, RNDr., Ph.D. (10.09.2024)