ADAPTIVE APPROXIMATION OF THE MONGE-KANTOROVICH PROBLEM VIA PRIMAL-DUAL GAP ESTIMATES

被引：5

作者：

Bartels, Soren ^{[1
]}

Schon, Patrick ^{[1
]}

机构：

[1] Albert Ludwigs Univ Freiburg, Abt Angew Math, Hermann Herder Str 10, D-79104 Freiburg, Germany

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2017年 / 51卷 / 06期

关键词：

Optimal transport; a posteriori error estimation; iterative solution; adaptive mesh refinement;

D O I：

10.1051/m2an/2017054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Monge-Kantorovich problem arises as a special case for linear cost functionals in optimal transportation problems. It leads to a convex minimization problem with limited regularity properties. The convergent finite element discretization and iterative solution of the problem and its dual are addressed. Based on these approximations a computable upper bound for the primal-dual gap is derived which is suitable for efficient local mesh refinement. Numerical experiments reveal a significant improvement of related adaptive methods.

引用

页码：2237 / 2261

页数：25

共 14 条

[1]

[Anonymous], 2015, SPRINGER SERIES COMP

[2]

[Anonymous], 1999, Current Developments in Mathematics

[3]

[Anonymous], 1998, PROB APPL S

[4]

[Anonymous], 2013, SERIES COMPUTATIONAL

[5]

[Anonymous], 2006, Report 102

[6] ON PARTIAL DIFFERENTIAL EQUATION U2/XUXX + 2UXUYUXY + U2/YUYY = 0 [J].

ARONSSON, G .

ARKIV FOR MATEMATIK, 1968, 7 (05) :395-&

[7] A mixed formulation of the Monge-Kantorovich equations [J].

Barrett, John W. ;

Prigozhin, Leonid .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2007, 41 (06) :1041-1060

[8]

Bartels S, 2015, MATH COMPUT, V84, P1217

[9] Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations [J].

Benamou, Jean-David ;

Carlier, Guillaume .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 167 (01) :1-26

[10] A mixed finite element method for a nonlinear Dirichlet problem [J].

Farhloul, M .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1998, 18 (01) :121-132

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