# Nonsmooth Problems of Calculus of Variations via Codifferentiation

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 4, page 1153-1180
- ISSN: 1292-8119

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topDolgopolik, Maxim. "Nonsmooth Problems of Calculus of Variations via Codifferentiation." ESAIM: Control, Optimisation and Calculus of Variations 20.4 (2014): 1153-1180. <http://eudml.org/doc/272835>.

@article{Dolgopolik2014,

abstract = {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.},

author = {Dolgopolik, Maxim},

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

keywords = {nonsmooth analysis; calculus of variations; codifferentiable function; problem of bolza; codifferentiable functions; Bolza problem; necessary optimality conditions},

language = {eng},

number = {4},

pages = {1153-1180},

publisher = {EDP-Sciences},

title = {Nonsmooth Problems of Calculus of Variations via Codifferentiation},

url = {http://eudml.org/doc/272835},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Dolgopolik, Maxim

TI - Nonsmooth Problems of Calculus of Variations via Codifferentiation

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 4

SP - 1153

EP - 1180

AB - 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.

LA - eng

KW - nonsmooth analysis; calculus of variations; codifferentiable function; problem of bolza; codifferentiable functions; Bolza problem; necessary optimality conditions

UR - http://eudml.org/doc/272835

ER -

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