Abstract (100 words or less): |  | The two decades of Interior Point Methods (IPMs) triggered a tremendous
theoretical and computational performance improvement in solving linear and
also nonlinear optimization problems. In this talk we reflect those achievements
and, in the light of the Klee-Minty example, illustrate the theoretical limitations
of these two dominant algorithm classes. The question "What next?" naturally arises. Understanding the strength and limitations of simplex methods and IPMs may lead to new classes of algorithms. |