Nonuniqueness of minimizers for semilinear optimal control problems

Understand

A counterexample to uniqueness of global minimizers of semilinear optimal control problems is given.

• The lack of uniqueness occurs for a special choice of the state-target in the cost functional.
• Our arguments show also that, for some state-targets, there exist local minimizers, which are not global.
• When this occurs, gradient-type algorithms may be trapped by the local minimizers, thus missing the global ones.