The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: , (1) where is a set of admissible controls and is the solution of the following equation: ; . (2). The results are nonlocal and new.
Keywords: functionals with deviating arguments, optimal control, Euler-Lagrange equation, financial market
@article{COCV_2008__14_2_381_0, author = {Tahraoui, Rabah and Samassi, Lassana}, title = {How to state necessary optimality conditions for control problems with deviating arguments ?}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {381--409}, publisher = {EDP-Sciences}, volume = {14}, number = {2}, year = {2008}, doi = {10.1051/cocv:2007058}, mrnumber = {2394516}, zbl = {1133.49002}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2007058/} }
TY - JOUR AU - Tahraoui, Rabah AU - Samassi, Lassana TI - How to state necessary optimality conditions for control problems with deviating arguments ? JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 381 EP - 409 VL - 14 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2007058/ DO - 10.1051/cocv:2007058 LA - en ID - COCV_2008__14_2_381_0 ER -
%0 Journal Article %A Tahraoui, Rabah %A Samassi, Lassana %T How to state necessary optimality conditions for control problems with deviating arguments ? %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 381-409 %V 14 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2007058/ %R 10.1051/cocv:2007058 %G en %F COCV_2008__14_2_381_0
Tahraoui, Rabah; Samassi, Lassana. How to state necessary optimality conditions for control problems with deviating arguments ?. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 2, pp. 381-409. doi : 10.1051/cocv:2007058. http://archive.numdam.org/articles/10.1051/cocv:2007058/
[1] On some optimal control problems governed by a state equation with memory. ESAIM: COCV (to appear) | EuDML | Numdam | MR
and ,[2] On the variational problem in the space of absolutely continuous functions. Nonlin. Anal. TMA 23 (1994) 1345-1351. | MR | Zbl
,[3] On the variation problem for a family of functionals in the space of absolutly continuous functions. Nonlin. Anal. TMA 26 (1996) 463-468. | MR | Zbl
and ,[4] On weak lower semi-continuity for a class of functionals with deviating argument. Nonlin. Anal. TMA 28 (1997) 2005-2015. | MR | Zbl
and ,[5] Variational methods for a class of nonlocal functionals. Comput. Math. Appl 37 (1999) 79-100. | MR | Zbl
, and ,[6] Measure theory and fine properties of functions. CRC Press, Inc. (1992). | MR | Zbl
and ,[7] Limits of control problems with weakly converging nonlocal input operators. Calculus of variations and optimal control (Haifa, 1998), Math. 411, Chapman Hall/CRC, Boca Raton, FL (2000) 117-140. | MR | Zbl
,[8] On reduction of variational problems to extremal problems without constraints. Russians mathematics 38 (1994) 37-47. | MR | Zbl
and ,[9] Optimal investment with taxes: an optimal control problem with endogeneous delay. Nonlin. Anal. TMA 37 (1999) 31-56. | MR | Zbl
, and ,[10] Optimal investment with taxes: an existence result. J. Math. Economics 33 (2000) 373-388. | MR | Zbl
, and ,[11] Variational and boundary value problems with deviating argument. Diff. Equ 6 (1970) 1349-1358. | MR | Zbl
,[12] On some necessary conditions of functionals with deviating argument. Nonlin. Anal. TMA 17 (1991) 457-464. | MR | Zbl
,[13] Boundary value problems for differential-difference equations arising from variational problems. Nonlin. Anal. TMA 18 (1992) 801-813. | MR | Zbl
,[14] Optimisation et commande optimale, méthodes mathématiques pour l'ingénieur, cours de l'École Polytechnique, Palaiseau, France.
and ,[15] Calculus of variation for funtionals with deviating arguments. Ph.D. thesis, University Paris-Dauphine, France (2004).
,[16] Comment établir des conditions nécessaires d'optimalité dans les problèmes de contrôle dont certains arguments sont déviés ? C.R. Acad. Sci. Paris Ser 338 (2004) 611-616. | MR | Zbl
and ,[17] Classical electrodynamics in term of direct interparticle actions. Rev. Modern Phys 21 (1949) 425-433. | MR | Zbl
and ,Cited by Sources: