Analysis of a Nonconvex Problem Related to Signal Selective Smoothing

1997 ◽  
Vol 07 (03) ◽  
pp. 313-328 ◽  
Author(s):  
M. Chipot ◽  
R. March ◽  
M. Rosati ◽  
G. Vergara Caffarelli
Keyword(s):  
Variational Problem ◽  
Existence Result ◽  
Minimizing Sequences ◽  
Qualitative Properties ◽  
Nonconvex Problem ◽  
Nonconvex Variational Problem ◽  
Selective Smoothing

We study some properties of a nonconvex variational problem. We fail to attain the infimum of the functional that has to be minimized. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original nonperturbed problem is analyzed numerically.

scholarly journals On the minimization of some nonconvex double obstacle problems

2003 ◽  
Vol 2003 (10) ◽  
pp. 535-551
Author(s):  
A. Elfanni
Keyword(s):  
Numerical Analysis ◽  
Variational Problem ◽  
Minimization Problem ◽  
Lipschitz Functions ◽  
Discrete Space ◽  
Obstacle Problems ◽  
Minimizing Sequences ◽  
Nonconvex Variational Problem ◽  
Admissible Functions

We consider a nonconvex variational problem for which the set of admissible functions consists of all Lipschitz functions located between two fixed obstacles. It turns out that the value of the minimization problem at hand is equal to zero when the obstacles do not touch each other; otherwise, it might be positive. The results are obtained through the construction of suitable minimizing sequences. Interpolating these minimizing sequences in some discrete space, a numerical analysis is then carried out.

scholarly journals Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem

2020 ◽  
Vol 13 (4) ◽  
pp. 1269-1290 ◽  
Author(s):  
Annalisa Iuorio ◽  
◽  
Christian Kuehn ◽  
Peter Szmolyan ◽  
Keyword(s):  
Variational Problem ◽  
Numerical Continuation ◽  
Nonconvex Variational Problem
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