Duality for the level sum of quasiconvex functions and applications

M. Volle

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 3, page 329-343
  • ISSN: 1292-8119

Abstract

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We study a quasiconvex conjugation that transforms the level sum of functions into the pointwise sum of their conjugates and derive new duality results for the minimization of the max of two quasiconvex functions. Following Barron and al., we show that the level sum provides quasiconvex viscosity solutions for Hamilton-Jacobi equations in which the initial condition is a general continuous quasiconvex function which is not necessarily Lipschitz or bounded.

How to cite

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Volle, M.. "Duality for the level sum of quasiconvex functions and applications." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 329-343. <http://eudml.org/doc/197352>.

@article{Volle2010,
abstract = { We study a quasiconvex conjugation that transforms the level sum of functions into the pointwise sum of their conjugates and derive new duality results for the minimization of the max of two quasiconvex functions. Following Barron and al., we show that the level sum provides quasiconvex viscosity solutions for Hamilton-Jacobi equations in which the initial condition is a general continuous quasiconvex function which is not necessarily Lipschitz or bounded. },
author = {Volle, M.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Level sum; quasiconvex duality; Galois correspondence; viscosity solution; Hamilton-Jacobi equations.; quasiconvex conjugation; level sum; duality; viscosity solutions; Hamilton-Jacobi equations},
language = {eng},
month = {3},
pages = {329-343},
publisher = {EDP Sciences},
title = {Duality for the level sum of quasiconvex functions and applications},
url = {http://eudml.org/doc/197352},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Volle, M.
TI - Duality for the level sum of quasiconvex functions and applications
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 329
EP - 343
AB - We study a quasiconvex conjugation that transforms the level sum of functions into the pointwise sum of their conjugates and derive new duality results for the minimization of the max of two quasiconvex functions. Following Barron and al., we show that the level sum provides quasiconvex viscosity solutions for Hamilton-Jacobi equations in which the initial condition is a general continuous quasiconvex function which is not necessarily Lipschitz or bounded.
LA - eng
KW - Level sum; quasiconvex duality; Galois correspondence; viscosity solution; Hamilton-Jacobi equations.; quasiconvex conjugation; level sum; duality; viscosity solutions; Hamilton-Jacobi equations
UR - http://eudml.org/doc/197352
ER -

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