Many problems in real life can be formulated as optimization problems. An important question in these optimization problems is then whether or not an optimal solution exists. Another important question is how it can be computed in an efficient way.
Therefore, important aspects in the area of optimization are the translation of a practical question into an optimization problem, the mathematical analysis of the problem (does there exist a solution at all?), the analysis of complexity of the algorithm to compute the optimal solution (how easy or difficult is it to compute a solution?).
Optimization plays a role in all aspects of society. From technology to university, from government to industry, everywhere the control of costs and the reduction of costs are crucial and techniques for optimization are indispensable. Mathematical optimization lies at the heart of many techniques in economy, econometrics, process control, and so on.