Short course on the Introduction to Mixed-Integer Nonlinear Optimization

Prof. Dr. Martin Schmidt, a Principal Investigator of the Research Training Group on Algorithmic Optimization, is offering a short course on the Introduction to Mixed-Integer Nonlinear Optimization.

The course will consist of 4 x 2  lectures of 90 minutes each on the following dates and times:

Wednesday,                     21 January 2020                     14:00 – 17:15                                              HS 10

Wednesday,                      5 February 2020                    14:00 – 17:15                                              HS 10

Wednesday,                     12 February 2020                   14:00 – 17:15                                              HS 10

Tuesday,                           18 February 2020                   14:00 – 17:15                                              HS 10

Course Abstract:

Mixed-integer nonlinear optimization problems (MINLPs) are of great importance in practice because they allow for two crucial modeling aspects. First, using integer variables makes it possible to model decision-making. Second, accurate modeling of real-world phenomena often leads to nonlinearities like in physics or in models of economies of scale. However, the combination of integer variables and nonlinearities also makes these problems extremely hard to solve for large-scale instances of real-world applications.

In this compact course, we introduce the class of convex and nonconvex MINLPs, discuss some MINLP-specific modeling tricks, and study the basic algorithms for solving MINLPs.

For a printout of this information, please click here.

Course outline:

Day 1: Introduction to the problem class of MINLPs
* Definition of problem class
* Convex vs. nonconvex MINLP
* Modeling examples
* Modeling techniques
* Good and bad formulations
* General algorithmic techniques for solving MINLPs

Day 2: Algorithmic techniques
* Nonlinear branch-and-bound
* Kelley’s cutting plane method
* Outer approximation
* LP-/NLP-based branch-and-bound

Day 3: Getting rid of what makes the problem hard
* MIP-based solution techniques
* NLP-based solution techniques

Day 4: Nonconvex MINLPs and Software
* Under- and overestimators
* expression trees
* Generic relaxation strategies for nonconvex MINLPs
* Spatial branch-and-bound
* Modeling software (GAMS, AMPL, Pyomo)
* Solvers