Geodesic
Differentiation of operators and optimality conditions in category interpretation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2010), pp. 66-76

Voir la notice de l'article provenant de la source Math-Net.Ru

The general extremum theory essentially uses properties of operator derivatives. As an example we consider a system described by a nonlinear elliptic equation. In this system with large values of the nonlinearity parameter and large dimension of the domain the control-state mapping is not Gateaux differentiable. For this reason one cannot immediately differentiate the optimality criterion and establish the necessary optimality conditions by classical methods. However the mentioned mapping is extendedly differentiable. This allows one to obtain optimality conditions without constraints on parameters of the system. Concluding the paper, we interpret the optimality conditions with classical and extended derivatives within the theory of categories.
Keywords: optimality conditions, operator derivatives, nonlinear elliptic equation, categories. 
@article{IVM_2010_2_a6,
     author = {S. Ya. Serovaiskii},
     title = {Differentiation of operators and optimality conditions in category interpretation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {66--76},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_2_a6/}
}
TY  - JOUR
AU  - S. Ya. Serovaiskii
TI  - Differentiation of operators and optimality conditions in category interpretation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 66
EP  - 76
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_2_a6/
LA  - ru
ID  - IVM_2010_2_a6
ER  - 
%0 Journal Article
%A S. Ya. Serovaiskii
%T Differentiation of operators and optimality conditions in category interpretation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 66-76
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_2_a6/
%G ru
%F IVM_2010_2_a6
S. Ya. Serovaiskii. Differentiation of operators and optimality conditions in category interpretation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2010), pp. 66-76. http://geodesic.mathdoc.fr/item/IVM_2010_2_a6/