Duality for the level sum of quasiconvex functions and applications
Duality for the level sum of quasiconvex functions and applications
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.
On a convolution operation obtained by adding level sets : classical and new results
The use of monotone norms in epigraphical analysis.
When some variational properties force convexity
The notion of adequate (resp. strongly adequate) function has been recently introduced to characterize the essentially strictly convex (resp. essentially firmly subdifferentiable) functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In this paper we provide various necessary and sufficient conditions in order that the lower semicontinuous hull of an extended real-valued function on a reflexive Banach space is essentially strictly convex. Some new results on nearest...
On the level sum of two convex functions on Banach spaces.
Epiconvergence D'une Suite De Sommes En Niveaux De Fonctions Convexes Epiconvergence of a Sequence of Level Sums of Convex Functions
We consider the problem of minimizing the max of two convex functions from both approximation and sensitivity point of view.This lead up to study the epiconvergence of a sequence of level sums of convex functions and the related dual problems.
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