Beschreibung
The goal of this course is to: - get a broader knowledge in the area of mathematical optimization with focus on (mixed) integer linear programming (MIP), - be able to model both academic and real world problems as MIPs, - be able to theoretically analyze and compare different mathematical programming formulations for a problem, - have knowledge on common methodology for solving MIPs, and - be able to develop practical solution algorithms using state-of-the-art MIP frameworks. Within the course we will consider the following content: - Overview on mathematical optimization (focus on mixed integer models, but also including non-linear and non-deterministic models) - Modeling (real world) problems as MIPs (basic techniques, modeling with exponentially many constraints and / or variables) - Solution methods for MIPs: Cutting plane method, branch-and-cut, Decomposition approaches (Langrangian decomposition, Dantzig-Wolfe decomposition) and corresponding solution methods (subgradient method, column generation, branch-and-price) - Theory of valid inequalities and further theoretical concepts: (Strong) valid inequalities (Chvatal-Gomory cuts, Gomory cuts, mixed integer cuts, cover cuts, theoretical concepts such as dominance, redundancy, facet defining cuts), "Well-solved" Problems properties, total unimodularity, optimization = separation) - Further issues in MIP computation and components of modern MIP solvers (presolving, primal heuristics, symmetry, frameworks) - Overview on further methods and extensions (stochastic- and robust optimization, non-linear programming, multiobjective optimization)Zeitraum | 1 März 2014 → 30 Juni 2014 |
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Gehalten am | TU Wien, Österreich |
Research Field
- Ehemaliges Research Field - Mobility Systems