| Paper ID | SPCOM-7.5 |
| Paper Title |
MIXED MONOTONIC PROGRAMMING FOR FAST GLOBAL OPTIMIZATION |
| Authors |
Bho Matthiesen, University of Bremen, Germany; Christoph Hellings, ETH Zurich, Switzerland; Eduard Jorswieck, Technische Universität Braunschweig, Germany; Wolfgang Utschick, Technical University of Munich, Germany |
| Session | SPCOM-7: Communication-enabled Applications |
| Location | Gather.Town |
| Session Time: | Friday, 11 June, 13:00 - 13:45 |
| Presentation Time: | Friday, 11 June, 13:00 - 13:45 |
| Presentation |
Poster
|
| Topic |
Signal Processing for Communications and Networking: [SPC-MIMO] Multiple-Input Multiple-Output |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| Abstract |
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient suboptimal heuristics are usually applied for practical implementations. However, there is also a strong interest in computing globally optimal solutions of nonconvex problems in offline simulations in order to benchmark faster suboptimal algorithms. Global solutions often rely on monotonicity properties. A common approach is to reformulate problems into a canonical monotonic optimization problem, but this often comes at the cost of nested optimizations, increased numbers of variables, and/or slow convergence. The framework of mixed monotonic programming (MMP) proposed in this paper avoids such performance-deteriorating reformulations by revealing hidden monotonicity properties directly in the original problem formulation. By means of a wide range of application examples from the area of signal processing for communications, we demonstrate that the novel MMP approach leads to tremendous complexity reductions compared to state-of-the-art methods for global optimization. However, the framework is not limited to optimizing communication systems, and we expect that similar speed-ups can be obtained for optimization problems from other areas of research as well. |
