Use this tag for any use of optimization within statistics.
In statistics, optimization if often used to select an estimator of a parameter by maximizing or minimizing some function of the data. One very common example of optimization in statistics is choosing an estimator which maximizes the joint density (or mass function) of the observed data; this is known as Maximum Likelihood Estimation (MLE).
Optimization is a large field and has many uses outside of estimation. In design of experiments we can choose a design by maximizing a certain determinant (D-optimality). In industrial statistics we can use a fitted response-surface model to optimize the economy or yield of a process. Wikipedia has an article https://en.wikipedia.org/wiki/Mathematical_optimization .