Consider the following Bolza problem:
We show that, under suitable assumptions onF, G, h, all optimal trajectories are bang-bang. The proof relies on a geometrical approach that works for every smooth two-dimensional manifold. As a corollary, we obtain existence results for nonconvex optimization problems.
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The authors thank Professor Arrigo Cellina for suggesting the problem and useful advice.
Communicated by R. Conti
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Crasta, G., Piccoli, B. Bang-bang property for Bolza problems in two dimensions. J Optim Theory Appl 83, 155–165 (1994). https://doi.org/10.1007/BF02191766
- Control theory
- Bolza problems
- bang-bang property
- nonconvex optimization problems