Mathematical Algorithmic Optimization - Otto-von-Guericke-University Magdeburg


Block Course: Mixed-integer Nonlinear Programming


Preliminary Program:

Time Monday, 29.3. Tuesday, 30.3. Wednesday, 31.3.
09h00-10h00 Sager: Introduction, Applications Diedam: Implementation Details Engelhart: Nonconvexities
10h00-10h15 Coffee break Coffee break Coffee break
10h15-11h15 Sager: Basic MINLP Algorithms Jung: Cutting Planes Kirches: Equilibrium Constraints
11h15-11h30 Coffee break Coffee break Coffee break
11h30-12h30 Sager: Continuous Optimization Sager: Modeling issues Sager: Mixed-integer Optimal Control
12h30-14h00 Lunch Lunch Lunch
14h00-18h00 Practical exercises: AMPL + MINLP algorithms Practical exercises: AMPL + cutting planes, different relaxations Practical exercises: nonconvex algorithms, collocation, MPECs


Mixed-Integer Nonlinear Programming (MINLP) is a sub-field of Mathematical Programming (MP) specializing in modeling and solving one of the most general (and hard) classes of optimization problems: namely, problems including both nonlinear terms and integer variables. There are countless applications: in energy production, chemical engineering, scheduling, software verification, quantum chemistry, geometry, bioinformatics, nuclear engineering, water distribution, dynamic processes involving discrete decisions such as gear choices or on/off valves, ...

Small and medium scale MINLPs can be solved using a Branch-and-Bound variant called "spatial Branch-and-Bound" (sBB), where branching is allowed on continuous as well as discrete variables that contribute to the gap between the original problem and its convex relaxation. For large-scale variants one often has to resort to heuristics, such as Rounding, Feasibility Pump, Local Branching; or exploit the problem structure to derive special-purpose methods.

Such special-purpose methods need to be applied, when the processes to be optimized are time-dependent. Mixed-integer optimal control problems (MIOCPs) are formally more general than MINLPs, but after a certain way of discretization a subclass of MINLPs with specific features that need to be exploited.

We revise some of these methods in theoretical lectures and apply them to challenging problems in afternoon hands-on practical exercises in the computer pool.


The course will be organized by Sebastian Sager, with support of Holger Diedam, Michael Engelhart, Michael Jung, and Christian Kirches.


Participation is free of charge and possible for all students in Heidelberg and doctoral students in optimization from Heidelberg and Trier upon registration, as well as for all participants of the EMBOCON project.

If you are interested in participating and are not a PhD student in mathematics from the aforementioned universities, please send me an email:

Else, please register here.

Last Modification: 2016-05-12 - Contact Person: Sebastian Sager - Impressum