157-9986/01 – Optimisation (O)
Gurantor department | Department of Systems Engineering | Credits | 10 |
Subject guarantor | doc. Mgr. Ing. František Zapletal, Ph.D. | Subject version guarantor | doc. Mgr. Ing. František Zapletal, Ph.D. |
Study level | postgraduate | Requirement | Compulsory |
Year | | Semester | winter + summer |
| | Study language | Czech |
Year of introduction | 2020/2021 | Year of cancellation | |
Intended for the faculties | EKF | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
The aim of this subject is to extend knowledge on and experience with mathematical modelling, with a special focus on optimization. Students will be able to solve complex optimization problems of convex, stochastic and fuzzy programming.
Teaching methods
Lectures
Individual consultations
Summary
The subject is divided into 4 parts, in which various subfields of optimization are explored:
A) Non-linear models and existence of their optimal solution (convex programming), Bender's decomposition.
B) Logical relationships between decision variables and constraints (OR, XOR, implication).
C) Stochastic programming - optimization with random parameters (static models, dynamic models - multi-stage models, non-anticipativity constraints, static and dynamic risk measures, coherent, convex and time-consistent risk measures,
D) fuzzy programming - optimization under uncertainty (with fuzzy parameters and relations - a way how to involve qualitative and subjective data.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
The final evaluation of a student is based on his/her activity during the semester and results of the oral exam.
E-learning
Information are provided to students at the lectures, through the LMS system. In LMS, there is an extended descriptions of the lectures and recommended literature.
Other requirements
Students must have a proactive approach and pass the oral exam.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1) Systemic approach, mathematical modelling.
2) Convex programming
3) Logical constraints
4) Risk measures
5) Single-stage and multi-stage stochastic programming.
6) Multi-stage stochastic programming.
7) Chance-constrained programming
8) Benders decomposition method.
9) Basics of fuzzy logic, algebra and set theory.
10) Possibilistic programming.
11) Flexible programming.
12) Intuitionistic fuzzy sets and their use in optimization.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.