In this paper multidimensional nonsmooth, nonconvex problems of the calculus of variations with codifferentiable integrand are studied. Special classes of codifferentiable functions, that play an important role in the calculus of variations, are introduced and studied. The codifferentiability of the main functional of the calculus of variations is derived. Necessary conditions for the extremum of a codifferentiable function on a closed convex set and its applications to the nonsmooth problems of the calculus of variations are described. Necessary optimality conditions in the main problem of the calculus of variations and in the problem of Bolza in the nonsmooth case are derived. Examples comparing presented results with other approaches to nonsmooth problems of the calculus of variations are given.
Mots-clés : nonsmooth analysis, calculus of variations, codifferentiable function, problem of bolza
@article{COCV_2014__20_4_1153_0,
author = {Dolgopolik, Maxim},
title = {Nonsmooth {Problems} of {Calculus} of {Variations} \protect\emph{via {}Codifferentiation}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1153--1180},
publisher = {EDP-Sciences},
volume = {20},
number = {4},
year = {2014},
doi = {10.1051/cocv/2014010},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014010/}
}
TY - JOUR AU - Dolgopolik, Maxim TI - Nonsmooth Problems of Calculus of Variations via Codifferentiation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 1153 EP - 1180 VL - 20 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014010/ DO - 10.1051/cocv/2014010 LA - en ID - COCV_2014__20_4_1153_0 ER -
%0 Journal Article %A Dolgopolik, Maxim %T Nonsmooth Problems of Calculus of Variations via Codifferentiation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 1153-1180 %V 20 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014010/ %R 10.1051/cocv/2014010 %G en %F COCV_2014__20_4_1153_0
Dolgopolik, Maxim. Nonsmooth Problems of Calculus of Variations via Codifferentiation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1153-1180. doi : 10.1051/cocv/2014010. http://www.numdam.org/articles/10.1051/cocv/2014010/
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