| Abstract: |
| In this talk, we consider the existence of Lagrange multipliers for infinite dimensional problems under G\^ateaux differentiability assumptions on the data. Our investigation follows two main steps: the proof of the existence of Lagrange multipliers under a calmness assumption on the constraints and the study of sufficient conditions, which only involve the G\^ateaux derivative of the function defining the constraint, that ensure this assumption.
We apply the abstract results to recover in a direct manner the optimality systems associated to two types of standard stochastic optimal control problems. |
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