What is mathematical optimization?

Mathematical optimization (also known as mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. This technique is commonly used for resource allocation, scheduling, and decision-making in various fields.