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Cursus: 201500372
201500372
Mathematical Optimization
Cursus informatie
Cursus201500372
Studiepunten (ECTS)5
CursustypeCursus
VoertaalEngels
Contactpersoondr. R.P. Hoeksma
E-mailr.p.hoeksma@utwente.nl
Docenten
Contactpersoon van de cursus
dr. R.P. Hoeksma
Docent
dr. R.P. Hoeksma
Docent
dr.ir. G.F. Post
Collegejaar2020
Aanvangsblok
2A
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
Cursusdoelen
After following the course the student is able to:
  • Explain how  the Gauss algorithm provides a proof of  main theorems in matrix theory.  
  • Describe how the Fourier-Motzkin algorithm leads to a constructive proof of the  Farkas Lemma.
  • Explain the basic idea behind strong duality of linear programs and the minmax theorem for matrix games.
  • Describe and sketch  the special  properties of convex sets and convex functions.  
  • Describe the theoretical basis of  different methods for solving smooth  (unconstrained) minimization problems and explain the working of these algorithms.
  • Apply the theoretical results to solve concrete (exercise) problems connected with the learned topics as well as to apply the  proofs  in a modified context.
Inhoud
Optimization problems appear in many real life  situations. The course aims to provide an introduction into algorithmic principles and fundamental ideas of linear and nonlinear  optimization. The course enables the student to follow more advanced courses in continuous and discrete optimization.
 
The course starts with the topic of algorithmic methods for solving linear equations and linear inequalities. The Farkas lemma provides the basis for duality results in linear optimization. Strong duality of linear programs, sensitivity and matrix games are treated. We then study the properties of convex sets and convex functions. These properties play an important role in optimization and applied analysis. We deal with the theoretical results and algorithmic methods for nonlinear (unconstrained) programming. In particular we discuss descent methods, methods of conjugate directions, Newton methods and modern Quasi-Newton algorithms.
 
Participating study
Bachelor Applied Mathematics
Module
Module 11
Verplicht materiaal
Course material
Script: Mathematical Optimization. It is available at Student Union shop.
Aanbevolen materiaal
-
Werkvormen
Overig onderwijs
AanwezigheidsplichtJa

Toetsen
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