401-3901-00L  Mathematical Optimization

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

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.