This paper studies the first-order behavior of the value function of a parametric optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Fréchet subdifferential of the value function of a parametric minimization problem, we derive a formula for computing the Fréchet subdifferential of the value function to a parametric optimal control problem. The obtained results improve and extend some previous results.
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Communicated by Boris Mordukhovich.
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Chieu, N.H., Kien, B.T. & Toan, N.T. Further Results on Subgradients of the Value Function to a Parametric Optimal Control Problem. J Optim Theory Appl 168, 785–801 (2016). https://doi.org/10.1007/s10957-011-9933-0
- Parametric optimal control
- Marginal function
- Value function
- Fréchet normal cone
- Fréchet subgradients
- Fréchet subdifferential