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: inf (u,v)𝒰 ad 0 1 ft,u(θ v (t)),u ' (t),v(t)dt, (1) where 𝒰 ad is a set of admissible controls and θ v is the solution of the following equation: {dθ(t) dt=g(t,θ(t),v(t)),t[0,1] ; θ(0)=θ 0 ,θ(t)[0,1]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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     pages = {381--409},
     publisher = {EDP-Sciences},
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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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