401-3901-00L Mathematical Optimization
|Semester||Autumn Semester 2014|
|Periodicity||yearly recurring 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.