scholarly journals Existence and monotonicity property of minimizers of a nonconvex variational problem with a second-order Lagrangian

2009 ◽  
Vol 25 (2) ◽  
pp. 687-699
Author(s):  
Kaizhi Wang ◽  
◽  
Yong Li ◽  
Keyword(s):  
Variational Problem ◽  
Monotonicity Property ◽  
Second Order ◽  
Nonconvex Variational Problem

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 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

scholarly journals Minimization of Vectors of Curvilinear Functionals on Second-Order Jet Bundle: Dual Program Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Mihai Postolache
Keyword(s):  
Variational Problem ◽  
Necessary Conditions ◽  
Optimization Theory ◽  
General Setting ◽  
Second Order ◽  
Mechanical Work ◽  
Program Theory ◽  
Jet Bundle ◽  
Dual Program ◽  
Suitable Framework

A previous paper (2011), Pitea and Postolache, considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multitime multiobjective variational problem, subject to PDE and/or PDI constraints. They have chosen the suitable framework offered by the second-order jet bundle, and initiated an optimization theory for this class of problems by introducing necessary conditions. As natural continuation of these results, the present work introduces a dual program theory, the general setting, and the theory which is new as a whole, containing our results.

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