# Duality for the level sum of quasiconvex functions and applications

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

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

## Access Full Article

top## Abstract

top## How to cite

topVolle, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.