# How to state necessary optimality conditions for control problems with deviating arguments?

Lassana Samassi; Rabah Tahraoui

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 14, Issue: 2, page 381-409
- ISSN: 1292-8119

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topSamassi, Lassana, and Tahraoui, Rabah. "How to state necessary optimality conditions for control problems with deviating arguments?." ESAIM: Control, Optimisation and Calculus of Variations 14.2 (2008): 381-409. <http://eudml.org/doc/250383>.

@article{Samassi2008,

abstract = {
The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form:
$\{\displaystyle\inf_\{\{\displaystyle(u,v)\in \{\cal U\}_\{ad\}\}\} \int_\{0\}^\{1\} f\left(t, u(\theta_v(t)),u^\{\prime\}(t),v(t)\right)\{\rm d\}t\}$, (1)
where $\{\cal U\}_\{ad\} $ is a set of admissible controls and $\theta_v$ is the solution of the following equation:
$\\{ \frac\{\{\rm d\}\theta(t)\}\{\{\rm d\}t\}=g(t,\theta(t),v(t)), t\in [0,1]$ ;
$\displaystyle\theta(0)=\theta_0, \theta(t)\in [0,1] \forall t$. (2).
The results are nonlocal and new.
},

author = {Samassi, Lassana, Tahraoui, Rabah},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Functionals with deviating arguments; optimal control; Euler-Lagrange equation; financial market; functionals with deviating arguments},

language = {eng},

month = {3},

number = {2},

pages = {381-409},

publisher = {EDP Sciences},

title = {How to state necessary optimality conditions for control problems with deviating arguments?},

url = {http://eudml.org/doc/250383},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Samassi, Lassana

AU - Tahraoui, Rabah

TI - How to state necessary optimality conditions for control problems with deviating arguments?

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/3//

PB - EDP Sciences

VL - 14

IS - 2

SP - 381

EP - 409

AB -
The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form:
${\displaystyle\inf_{{\displaystyle(u,v)\in {\cal U}_{ad}}} \int_{0}^{1} f\left(t, u(\theta_v(t)),u^{\prime}(t),v(t)\right){\rm d}t}$, (1)
where ${\cal U}_{ad} $ is a set of admissible controls and $\theta_v$ is the solution of the following equation:
$\{ \frac{{\rm d}\theta(t)}{{\rm d}t}=g(t,\theta(t),v(t)), t\in [0,1]$ ;
$\displaystyle\theta(0)=\theta_0, \theta(t)\in [0,1] \forall t$. (2).
The results are nonlocal and new.

LA - eng

KW - Functionals with deviating arguments; optimal control; Euler-Lagrange equation; financial market; functionals with deviating arguments

UR - http://eudml.org/doc/250383

ER -

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