Optimization is an essential tool for decision making and it is extensively used in the design and operation of systems. In its most common form, optimization considers the maximization of an objective function with respect to the decision variables, which may be subject to constraints. Therein, the objective function represents the utility or benefit gained by a decision, whereas the constraints enforce any relevant side conditions. The computational effort to determine an optimal decision is highly dependent on the mathematical structure of the optimization problem. While a closed-form solution may be attainable in certain cases, most practical problems require the use of iterative algorithms. For a broad class of problems, i.e., convex optimization problems, efficient polynomial time algorithms exist. Besides algorithms, there also exist analytical tools including optimality conditions and duality that may be utilized to characterize properties of the solution or support problem decompositions and parallel processing.

Optimization is used in the following fields of research at our institute:

• Interference-Limited Communication Systems
• Radar and DoA Estimation
• Multi-User MIMO Communications
• Optimization in Power Systems

To learn more about optimization we kindly refer to the following lectures offered at our institute:

• Adaptive and Array Signal Processing
• Convex Optimization
• Convex Optimization Laboratory
• MIMO Systems
• Statistical Signal Processing