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Notes
- 1.
Other types of constraints advocated in Sect 1.1.2 might also be considered but we limit ourselves to those introduced hereafter.
- 2.
The reader may refer to Sect. A.1.4 for notations such as \(\nabla _{u} g\), \(\nabla _{x}g\), \(\nabla _{u}f\) and \(\nabla _{x}f\), and especially to Remark A.4 regarding the last two ones.
- 3.
Observe that this holds true even if \(\lambda \) out of (5.13b) is non unique, that is, even if \(\nabla _{x} f(u,x)\) is singular.
- 4.
Auto-Regressive Moving Average.
- 5.
When \(\varOmega \) is finite, this claim is straightforward; otherwise it is rather technical to prove [149].
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Carpentier, P., Chancelier, JP., Cohen, G., De Lara, M. (2015). Optimality Conditions for Stochastic Optimal Control (SOC) Problems. In: Stochastic Multi-Stage Optimization. Probability Theory and Stochastic Modelling, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-319-18138-7_5
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