Approximations of Optimization-Related Problems in Terms of Variational Convergence

2015 ◽  
Vol 44 (2) ◽  
pp. 399-417 ◽  
Author(s):  
Huynh Thi Hong Diem ◽  
Phan Quoc Khanh
Keyword(s):  
Variational Convergence

scholarly journals Approximations of Variational Problems in Terms of Variational Convergence

2017 ◽  
Vol 20 (K2) ◽  
pp. 107-116
Author(s):  
Diem Thi Hong Huynh
Keyword(s):  
Multiobjective Optimization ◽  
Metric Space ◽  
Metric Spaces ◽  
Equilibrium Problems ◽  
Variational Problems ◽  
Dimensional Case ◽  
Variational Convergence ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Definition Of

We show first the definition of variational convergence of unifunctions and their basic variational properties. In the next section, we extend this variational convergence definition in case the functions which are defined on product two sets (bifunctions or bicomponent functions). We present the definition of variational convergence of bifunctions, icluding epi/hypo convergence, minsuplop convergnece and maxinf-lop convergence, defined on metric spaces. Its variational properties are also considered. In this paper, we concern on the properties of epi/hypo convergence to apply these results on optimization proplems in two last sections. Next we move on to the main results that are approximations of typical and important optimization related problems on metric space in terms of the types of variational convergence are equilibrium problems, and multiobjective optimization. When we applied to the finite dimensional case, some of our results improve known one.

scholarly journals Variational convergence over metric spaces

2008 ◽  
Vol 360 (01) ◽  
pp. 35-76 ◽  
Author(s):  
Kazuhiro Kuwae ◽  
Takashi Shioya
Keyword(s):  
Metric Spaces ◽  
Variational Convergence

scholarly journals A characterization of variational convergence for segmentation problems

1995 ◽  
Vol 1 (3) ◽  
pp. 347-369 ◽  
Author(s):  
Micol Amar ◽  
◽  
Andrea Braides ◽  
Keyword(s):  
Variational Convergence

Some variational convergence results with applications to evolution inclusions

2006 ◽  
pp. 33-73 ◽  
Author(s):  
Charles Castaing ◽  
Paul Raynaud de Fitte ◽  
Anna Salvadori
Keyword(s):  
Variational Convergence ◽  
Evolution Inclusions ◽  
Convergence Results

Coupling proximal methods and variational convergence

1993 ◽  
Vol 38 (3) ◽  
pp. 269-280 ◽  
Author(s):  
Abdellatif Moudafi
Keyword(s):  
Proximal Methods ◽  
Variational Convergence

scholarly journals Uniform convexity and variational convergence

2014 ◽  
Vol 75 ◽  
pp. 205-231
Author(s):  
V. V. Zhikov ◽  
S. E. Pastukhova
Keyword(s):  
Uniform Convexity ◽  
Variational Convergence

scholarly journals A MATHEMATICAL MODEL FOR A PSEUDO-PLASTIC WELDING JOINT

2009 ◽  
Vol 07 (03) ◽  
pp. 243-267 ◽  
Author(s):  
OANA IOSIFESCU ◽  
PONGPOL JUNTHAREE ◽  
CHRISTIAN LICHT ◽  
GÉRARD MICHAILLE
Keyword(s):  
Mathematical Model ◽  
Asymptotic Behavior ◽  
Energy Density ◽  
Thin Layer ◽  
Intermediate Layer ◽  
Variational Convergence ◽  
Accurate Model ◽  
Welding Joint ◽  
Bulk Energy ◽  
Plastic Welding

An elementary situation in welding involves the perfect assembly of two adherents and a strong adhesive occupying a thin layer. The bulk energy density of the hyperelastic adherents grows superlinearly while that of the pseudo-plastic adhesive grows linearly with a stiffness of the order of the inverse of its thickness ε. We propose a simplified but accurate model by studying the asymptotic behavior, when ε goes to zero, through variational convergence methods: at the limit, the intermediate layer is replaced by a pseudo-plastic interface which allows cracks to appear.

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