A finite dimensional linear programming approximation of Mather's variational problem
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, p. 1094-1109

We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693-702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.

DOI : https://doi.org/10.1051/cocv/2009039
Classification:  37J50,  49Q20,  49N60,  74P20,  65K10
Keywords: Mather problem, minimal measures, linear programming, Γ-convergence
@article{COCV_2010__16_4_1094_0,
     author = {Granieri, Luca},
     title = {A finite dimensional linear programming approximation of~Mather's variational problem},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {4},
     year = {2010},
     pages = {1094-1109},
     doi = {10.1051/cocv/2009039},
     zbl = {1205.37077},
     mrnumber = {2744164},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2010__16_4_1094_0}
}
Granieri, Luca. A finite dimensional linear programming approximation of Mather's variational problem. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, pp. 1094-1109. doi : 10.1051/cocv/2009039. http://www.numdam.org/item/COCV_2010__16_4_1094_0/

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