Optimization Algorithms
System-theoretic Analysis and Design of Algorithms
Optimization algorithms are frequently used to solve decision making and control problems. Control engineering methods, on the other hand, are rarely used in optimization, regardless of the facts that control engineering is devoted to the analysis and design of dynamical systems, and that optimization algorithms are dynamical systems.
In our research, we analyze and design optimization algorithms using methods from systems and control theory. In particular, we study discrete-time but also continuous-time (analog) optimization algorithms, and we employ robust and geometric control theory to analyze and design a novel generation of optimization algorithms.
Related Publications
| Title | Authors and Contributors |
|---|---|
| Robust and structure exploiting optimisation algorithms: an integral quadratic constraint approach In: International journal of control, 94 (2020), 11, 2956-2979 Journal Article [DOI: 10.1080/00207179.2020.1745286] | Michalowsky, Simon (Corresponding author) Scherer, Carsten Ebenbauer, Christian Johannes |
| Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions (2020) Preprint | Gramlich, Dennis Ebenbauer, Christian Johannes Scherer, Carsten W. |
| The multidimensional n-th order heavy ball method and its application to extremum seeking In: Proc. of the 53rd IEEE Conference on Decision and Control (CDC), Los Angeles, USA (2014), 2660-2666 Contribution to a book, Contribution to a conference proceedings [DOI: 10.1109/CDC.2014.7039796] | Michalowsky, Simon Ebenbauer, Christian Johannes |
| On a Class of Smooth Optimization Algorithms with Applications in Control In: Proc. of the 4th IFAC NMPC Conference 2012, Leeuwenhorst, Netherlands (2012), 291-298 Contribution to a conference proceedings | Dürr, H. B. Ebenbauer, Christian Johannes |
Distributed Control and Optimization
The solution of large-scale optimization problems by a group of agents that can exchange information through a communication network has matured into an important area of research. Distributed optimization problems are found in many applications such as optimal power dispatch problems in Smart Grids, distributed Machine Learning or formation control of small mobile robots. However, existing algorithms solving such problems often have severely limiting requirements on the problem class as well as the communication structure, e.g., consensus-type problems or undirected information flow.
In our research, we are developing new approaches to distributed optimization, both in continuous-time as well as discrete-time. These are applicable to a large class of constrained optimization problems under mild assumptions on the underlying communication network as well as on the problem structure. In particular, we employ saddle-point (primal-dual) algorithms for centralized convex optimization and use Lie bracket approximation to derive distributed approximations thereof.
Related Publications
| Title | Authors and Contributors |
|---|---|
| A Lie bracket approximation approach to distributed optimization over directed graphs In: Automatica : a journal of IFAC, the International Federation of Automatic Control, 112 (2019), 108691 Journal Article [DOI: 10.1016/j.automatica.2019.108691] | Michalowsky, Simon (Corresponding author) Gharesifard, Bahman Ebenbauer, Christian Johannes |
| Distributed Optimization over Directed Graphs with the help of Lie Brackets In: IFAC-PapersOnLine, 50 (2017), 1, 15343-15348 Contribution to a conference proceedings, Journal Article [DOI: 10.1016/j.ifacol.2017.08.2456] | Ebenbauer, Christian Johannes (Corresponding author) Michalowsky, Simon (Corresponding author) Grushkovskaya, Victoria (Corresponding author) Gharesifard, Bahman (Corresponding author) |
| Multi-Agent Coordination with Lagrangian Measurements In: Proc. of the 6th IFAC Workshop on Distributed Estimation and Control in Networked Systems, Tokyo, Japan (2016), 115-120 Contribution to a conference proceedings | Grushkovskaya, V. Ebenbauer, Christian Johannes |