How to state necessary optimality conditions for control problems with deviating arguments ?
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 381-409.

The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: $\underset{\left(u,v\right)\in {𝒰}_{ad}}{inf}{\int }_{0}^{1}f\left(t,u\left({\theta }_{v}\left(t\right)\right),{u}^{\text{'}}\left(t\right),v\left(t\right)\right)\mathrm{d}t$, (1) where ${𝒰}_{ad}$ is a set of admissible controls and ${\theta }_{v}$ is the solution of the following equation: $\left\{\frac{\mathrm{d}\theta \left(t\right)}{\mathrm{d}t}=g\left(t,\theta \left(t\right),v\left(t\right)\right),t\in \left[0,1\right]$ ; $\theta \left(0\right)={\theta }_{0},\theta \left(t\right)\in \left[0,1\right]\forall t$. (2). The results are nonlocal and new.

DOI : https://doi.org/10.1051/cocv:2007058
Classification : 49J15,  49J22,  49J25,  49J45,  49K15,  49K25,  49K22,  34K35,  47E05,  91B26,  91B28,  93C15
Mots clés : functionals with deviating arguments, optimal control, Euler-Lagrange equation, financial market
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author = {Tahraoui, Rabah and Samassi, Lassana},
title = {How to state necessary optimality conditions for control problems with deviating arguments ?},
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Tahraoui, Rabah; Samassi, Lassana. How to state necessary optimality conditions for control problems with deviating arguments ?. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 381-409. doi : 10.1051/cocv:2007058. http://www.numdam.org/articles/10.1051/cocv:2007058/

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