# Category:Objective characterization

This category lists all different characterizations of control goals, in particular of the objective function and special kinds of constraints.

The optimization problem in the problem description is described by means of an objective functional $\Phi[\cdot]$ and inequality constraints $C[\cdot]$ and equality constraints $\Gamma[\cdot]$. The constraints come in form of multipoint constraints that are defined on a time grid $t_0 \le t_1 \le \dots \le t_m = t_f$, and of path-constraints that need to hold almost everywhere on the time horizon. The equality constraints $\Gamma[\cdot]$ will often fix the initial values or impose a periodicity constraint. In this classification we assume all functions to be sufficiently often differentiable.

In the future, the classification will also include problems with nondifferentiable objective functions, multiple objectives, online control tasks including feedback, indication of nonconvexities, and more characteristics that allow for a specific choice of test instances.

## Subcategories

This category has the following 7 subcategories, out of 7 total.