401-3901-00L  Mathematical Optimization

Semester Autumn Semester 2017
Lecturers R. Weismantel
Periodicity yearly course
Language of instruction English



Catalogue data

Abstract Mathematical treatment of diverse optimization techniques.
Objective Advanced optimization theory and algorithms.
Content 1) 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.
Literature 1) 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 / Notice Linear algebra.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits 11 credits
Examiners R. Weismantel
Type session examination
Language of examination English
Course attendance confirmation required No
Repetition The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination written 120 minutes
Written aids 10 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

Number Title Hours Lecturers
401-3901-00 V Mathematical Optimization 4 hrs
Mon 13-15 HG E 1.1 »
Thu 10-12 HG D 5.2 »
R. Weismantel
401-3901-00 U Mathematical Optimization 2 hrs
Fri 10-12 HG E 1.1 »
R. Weismantel

Restrictions

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