401-3901-00L  Mathematical Optimization

SemesterAutumn Semester 2017
LecturersR. Weismantel
Periodicityyearly course
Language of instructionEnglish



Catalogue data

AbstractMathematical treatment of diverse optimization techniques.
ObjectiveAdvanced optimization theory and algorithms.
Content1) Linear optimization: The geometry of linear programming, the simplex method for solving linear programming problems, Farkas' Lemma and infeasibility certificates, duality theory of linear programming.

2) Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization.

3) Integer optimization: Ties between linear and integer optimization, total unimodularity, complexity theory, cutting plane theory.

4) Combinatorial optimization: Network flow problems, structural results and algorithms for matroids, matchings, and, more generally, independence systems.
Literature1) D. Bertsimas & R. Weismantel, "Optimization over Integers". Dynamic Ideas, 2005.

2) A. Schrijver, "Theory of Linear and Integer Programming". John Wiley, 1986.

3) D. Bertsimas & J.N. Tsitsiklis, "Introduction to Linear Optimization". Athena Scientific, 1997.

4) Y. Nesterov, "Introductory Lectures on Convex Optimization: a Basic Course". Kluwer Academic Publishers, 2003.

5) C.H. Papadimitriou, "Combinatorial Optimization". Prentice-Hall Inc., 1982.
Prerequisites / NoticeLinear algebra.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits11 credits
ExaminersR. Weismantel
Typesession examination
Language of examinationEnglish
Course attendance confirmation requiredNo
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 120 minutes
Written aids10 one-sided A4 sheets or 5 two-sided A4 sheets, hand- or typewritten.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
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Courses

NumberTitleHoursLecturers
401-3901-00 VMathematical Optimization4 hrs
Mon13-15HG E 1.1 »
Thu10-12HG D 5.2 »
R. Weismantel
401-3901-00 UMathematical Optimization2 hrs
Fri10-12HG E 1.1 »
R. Weismantel

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Offered in

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Spatial Development and Infrastructure Systems MasterRecommended Electives of Master Degree ProgrammeWInformation
Computational Science and Engineering BachelorElectivesWInformation
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Statistics MasterStatistical and Mathematical CoursesWInformation