Title:  Optimization 

Code:  OPM 

Ac.Year:  2017/2018 

Term:  Summer 

Curriculums:  

Language of Instruction:  Czech 

Credits:  4 

Completion:  credit+exam (written&verbal) 

Type of instruction:  Hour/sem  Lectures  Seminar Exercises  Laboratory Exercises  Computer Exercises  Other 

Hours:  26  0  0  13  0 

 Exams  Tests  Exercises  Laboratories  Other 

Points:  60  0  0  0  40 



Guarantor:  Popela Pavel, RNDr., Ph.D. (UM OSO) 

Lecturer:  Popela Pavel, RNDr., Ph.D. (UM OSO) 
Faculty:  Faculty of Mechanical Engineering BUT 

Department:  Department of Mathematics, section of Statistics and Optimalization FME BUT 


Learning objectives: 

  The course objective is to emphasize optimization modelling together with solution methods. It involves problem analysis, model building, model description and transformation, and the choice of the algorithm. Introduced methods are based on the theory and illustrated by geometrical point of view. 
Description: 

  The course presents fundamental optimization models and methods for solving of technical problems. The principal ideas of mathematical programming are discussed: problem analysis, model building, solution search, and the interpretation of results. The course mainly deals with linear programming (polyhedral sets, simplex method, duality) and nonlinear programming (convex analysis, KarushKuhnTucker conditions, selected algorithms). Basic information about network flows and integer programming is included as well as further generalizations of studied mathematical programs. 
Knowledge and skills required for the course: 

  Fundamental knowledge of principal concepts of Calculus and Linear Algebra in the scope of the mathematical engineering curriculum is assumed. 
Learning outcomes and competences: 

  The course is designed for mathematical engineers and it is useful for applied sciences students. Students will learn the theoretical background of fundamental topics in optimization (especially linear and nonlinear programming). They will also made familiar with useful algorithms and interesting applications. 
Syllabus of lectures: 


 Introductory models (IM): problem formulation, problem analysis, model design, theoretical properties.
 IM: visualization, algorithms, software, postprocessing in optimization
 Linear programming (LP): Convex and polyhedral sets.
 LP: Set of feasible solutions and theoretical foundations.
 LP: The Simplex method.
 LP: Duality and parametric analysis.
 Network flow models.
 Basic concepts of integer programming.
 Nonlinear programming (NLP): Convex functions and their properties.
 NLP: Unconstrained optimization. Numerical methods for univariate optimization.
 NLP: Unconstrained optimization and related numerical methods for multivariate optimization.
 NLP: Constrained optimization and KarushKuhnTucker conditions.
 NLP: Constrained optimization and related numerical methods for multivariate optimization.

Study literature: 


 Klapka a kol.: Metody operačního výzkumu, Brno 2001 (in Czech).
 Dvořák a kol.: Operační analýza, Brno, 1996 (in Czech).
 Charamza a kol.: Modelovací systém GAMS, Praha 1994 (in Czech).
 Dupačová et al.: Lineárne programovanie, Alfa, 1990 (in Slovak).
 Bazaraa et al.: Linear Programming and Network Flows, Wiley 1990.
 Bazaraa et al.: Nonlinear Programming, Wiley 1993.

Controlled instruction: 

  The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments. 
Progress assessment: 

  The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments. 
Exam prerequisites: 

  Gaining at least 20 points during the semester. 
