Mathematical optimisation deals with the task of creating an optimal solution from a number of appropriate solutions.
The number of appropriate solutions is generally defined by constraints which are applied to the decision variables. Optimality is defined by entering a target function over the decision variable. The main task is to maximize or minimize the target function. From this, we get special mathematical optimisation problems, depending on the structure of the decision variable or the constraints. Optimisation processes were important in the areas of military applications and the problems associated with this during the Second World War. Today, optimisation processes are used in various areas of logistics, industry and economics.
Modelling a practical request as an optimisation task and then categorising this as a linear, non-linear, vertical, discrete, geometric, continual or parametric optimisation is an important step towards finding a solution. This modelling process forms the basis for the software-based implementation of said solution. Every different optimisation problem requires a specially tailored solution algorithm (solver).
Modern optimisation processes can solve problems using many thousands of variables and side conditions.