Event

Many optimization problems from economics, engineering and natural sciences are modeled with continuous as well as with discrete variables. Examples are the energy minimal design of a chemical process in which several reactors may be switched on or off, portfolio optimization with limitations on the number of securities, the choice of locations to serve customers at minimum cost, and the optimal design of vote allocations in election procedures. For the algorithmic identification of optimal points of such problems an interaction of ideas from discrete as well as continuous optimization is necessary.

The lecture focusses on mixed-integer nonlinear optimization problems and is structured as follows:

• Continuous relaxation and error bounds for roundings
• Branch-and-Bound for convex and nonconvex problems
• Generalized Benders decomposition
• Outer approximation methods
• Lagrange relaxation
• Dantzig-Wolfe decomposition
• Heuristics

The lecture is accompanied by exercises which, amongst others, offers the opportunity to implement and to test some of the methods on practically relevant examples.

Remark:

The treatment of mixed-integer linear optimization problems forms the contents of the lecture "Mixed-integer Programming I".

Learning objectives:

The student

• knows and understands the fundamentals of nonlinear mixed integer programming,
• is able to choose, design and apply modern techniques of nonlinear mixed integer programming in practice.