## Multi-Objective Optimization

Many optimization problems have multiple competing objectives. These competing objectives are part of the trade-off that defines an optimal solution. Sometimes these competing objectives have separate priorities where one objective should be satisfied *before* another objective is even considered. This especially arises in model predictive control or other types of dynamic optimization problems. There are competing objectives with a ranked hierarchy. The highest level objectives are satisfied first followed by lower ranked objectives if there are additional degrees of freedom available. The l1-norm objective is a natural way to explicitly rank objectives and simultaneously optimize multiple priorities with a single optimization problem.

#### Exercise

Consider examples of safety, environmental, and economic constraints or objectives. Which are most important and why?

For the following multi-objective optimization problem, sketch a possible optimal trajectory.