메뉴 건너뛰기




Volumn 277, Issue 6, 2019, Pages 1868-1957

A variational approach to the mean field planning problem

Author keywords

Kantorovich duality; Mean field planning; Optimal transport; Superposition principle

Indexed keywords


EID: 85066492601     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2019.04.011     Document Type: Article
Times cited : (58)

References (32)
  • 1
    • 84858650669 scopus 로고    scopus 로고
    • Mean field games: numerical methods for the planning problem
    • Achdou, Yves, Camilli, Fabio, Capuzzo-Dolcetta, Italo, Mean field games: numerical methods for the planning problem. SIAM J. Control Optim. 50:1 (2012), 77–109.
    • (2012) SIAM J. Control Optim. , vol.50 , Issue.1 , pp. 77-109
    • Achdou, Y.1    Camilli, F.2    Capuzzo-Dolcetta, I.3
  • 2
    • 70349507985 scopus 로고    scopus 로고
    • Geodesics in the space of measure-preserving maps and plans
    • Ambrosio, Luigi, Figalli, Alessio, Geodesics in the space of measure-preserving maps and plans. Arch. Ration. Mech. Anal. 194:2 (2009), 421–462.
    • (2009) Arch. Ration. Mech. Anal. , vol.194 , Issue.2 , pp. 421-462
    • Ambrosio, L.1    Figalli, A.2
  • 3
    • 31744443874 scopus 로고    scopus 로고
    • Gradient Flows in Metric Spaces and in the Space of Probability Measures
    • second edition Birkhäuser Verlag Basel
    • Ambrosio, Luigi, Gigli, Nicola, Savaré, Giuseppe, Gradient Flows in Metric Spaces and in the Space of Probability Measures. second edition Lectures in Mathematics ETH Zürich, 2008, Birkhäuser Verlag, Basel.
    • (2008) Lectures in Mathematics ETH Zürich
    • Ambrosio, L.1    Gigli, N.2    Savaré, G.3
  • 4
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • Benamou, Jean-David, Brenier, Yann, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84:3 (2000), 375–393.
    • (2000) Numer. Math. , vol.84 , Issue.3 , pp. 375-393
    • Benamou, J.-D.1    Brenier, Y.2
  • 6
    • 33845497931 scopus 로고    scopus 로고
    • Optimal mass transportation and Mather theory
    • Bernard, Patrick, Buffoni, Boris, Optimal mass transportation and Mather theory. J. Eur. Math. Soc. (JEMS) 9:1 (2007), 85–121.
    • (2007) J. Eur. Math. Soc. (JEMS) , vol.9 , Issue.1 , pp. 85-121
    • Bernard, P.1    Buffoni, B.2
  • 7
    • 34547254091 scopus 로고    scopus 로고
    • Measure Theory. Vol. I
    • Springer-Verlag Berlin
    • Bogachev, Vladimir Igorevich, Measure Theory. Vol. I. 2007, Springer-Verlag, Berlin.
    • (2007)
    • Bogachev, V.I.1
  • 8
    • 34547254091 scopus 로고    scopus 로고
    • Measure Theory. Vol. II
    • Springer-Verlag Berlin
    • Bogachev, Vladimir Igorevich, Measure Theory. Vol. II. 2007, Springer-Verlag, Berlin.
    • (2007)
    • Bogachev, V.I.1
  • 11
    • 84885675830 scopus 로고    scopus 로고
    • Geodesics for a class of distances in the space of probability measures
    • Cardaliaguet, Pierre, Carlier, Guillaume, Nazaret, Bruno, Geodesics for a class of distances in the space of probability measures. Calc. Var. Partial Differential Equations 48:2,3 (2013), 395–420.
    • (2013) Calc. Var. Partial Differential Equations , vol.48 , Issue.2-3 , pp. 395-420
    • Cardaliaguet, P.1    Carlier, G.2    Nazaret, B.3
  • 13
    • 84992539178 scopus 로고    scopus 로고
    • First order mean field games with density constraints: pressure equals price
    • Cardaliaguet, Pierre, Mészáros, Alpár R., Santambrogio, Filippo, First order mean field games with density constraints: pressure equals price. SIAM J. Control Optim. 54:5 (2016), 2672–2709.
    • (2016) SIAM J. Control Optim. , vol.54 , Issue.5 , pp. 2672-2709
    • Cardaliaguet, P.1    Mészáros, A.R.2    Santambrogio, F.3
  • 14
    • 0003211244 scopus 로고
    • Convex Analysis and Measurable Multifunctions
    • Springer-Verlag Berlin
    • Castaing, Charles, Valadier, Michel, Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580, 1977, Springer-Verlag, Berlin.
    • (1977) Lecture Notes in Mathematics , vol.580
    • Castaing, C.1    Valadier, M.2
  • 15
    • 85044332791 scopus 로고    scopus 로고
    • Unbalanced optimal transport: dynamic and Kantorovich formulations
    • Chizat, Lénaïc, Peyré, Gabriel, Schmitzer, Bernhard, Vialard, François-Xavier, Unbalanced optimal transport: dynamic and Kantorovich formulations. J. Funct. Anal. 274:11 (2018), 3090–3123.
    • (2018) J. Funct. Anal. , vol.274 , Issue.11 , pp. 3090-3123
    • Chizat, L.1    Peyré, G.2    Schmitzer, B.3    Vialard, F.-X.4
  • 16
    • 0003725571 scopus 로고    scopus 로고
    • Convex Analysis and Variational Problems
    • English edition Society for Industrial and Applied Mathematics (SIAM) Philadelphia, PA translated from the French
    • Ekeland, Ivar, Témam, Roger, Convex Analysis and Variational Problems. English edition Classics in Applied Mathematics, vol. 28, 1999, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA translated from the French.
    • (1999) Classics in Applied Mathematics , vol.28
    • Ekeland, I.1    Témam, R.2
  • 18
    • 85067201545 scopus 로고    scopus 로고
    • The planning problem in mean field games as regularized mass transport
    • arXiv preprint
    • Graber, P. Jameson, Mészáros, Alpár R., Silva, Francisco J., Tonon, Daniela, The planning problem in mean field games as regularized mass transport. arXiv preprint arXiv:1811.02706, 2018.
    • (2018)
    • Graber, P.J.1    Mészáros, A.R.2    Silva, F.J.3    Tonon, D.4
  • 19
    • 33750627999 scopus 로고    scopus 로고
    • Jeux à champ moyen. I. Le cas stationnaire
    • Lasry, Jean-Michel, Lions, Pierre-Louis, Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343:9 (2006), 619–625.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.9 , pp. 619-625
    • Lasry, J.-M.1    Lions, P.-L.2
  • 20
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. II. Horizon fini et contrôle optimal
    • Lasry, Jean-Michel, Lions, Pierre-Louis, Jeux à champ moyen. II. Horizon fini et contrôle optimal. C. R. Math. Acad. Sci. Paris 343:10 (2006), 679–684.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.343 , Issue.10 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 21
    • 34047127341 scopus 로고    scopus 로고
    • Mean field games
    • Lasry, Jean-Michel, Lions, Pierre-Louis, Mean field games. Jpn. J. Math. 2:1 (2007), 229–260.
    • (2007) Jpn. J. Math. , vol.2 , Issue.1 , pp. 229-260
    • Lasry, J.-M.1    Lions, P.-L.2
  • 22
    • 84855241746 scopus 로고    scopus 로고
    • From the Schrödinger problem to the Monge-Kantorovich problem
    • Léonard, Christian, From the Schrödinger problem to the Monge-Kantorovich problem. J. Funct. Anal. 262:4 (2012), 1879–1920.
    • (2012) J. Funct. Anal. , vol.262 , Issue.4 , pp. 1879-1920
    • Léonard, C.1
  • 23
    • 85038116451 scopus 로고    scopus 로고
    • Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures
    • Liero, Matthias, Mielke, Alexander, Savaré, Giuseppe, Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures. Invent. Math. 211:3 (2018), 969–1117.
    • (2018) Invent. Math. , vol.211 , Issue.3 , pp. 969-1117
    • Liero, M.1    Mielke, A.2    Savaré, G.3
  • 24
    • 84865537156 scopus 로고    scopus 로고
    • Cours au collège de france
    • année 2009-2010, Technical report
    • Lions, Pierre-Louis, Cours au collège de france. année 2009-2010, Technical report www.college-de-france.fr.
    • Lions, P.-L.1
  • 25
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • McCann, Robert J., A convexity principle for interacting gases. Adv. Math. 128:1 (1997), 153–179.
    • (1997) Adv. Math. , vol.128 , Issue.1 , pp. 153-179
    • McCann, R.J.1
  • 26
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: the porous medium equation
    • Otto, Felix, The geometry of dissipative evolution equations: the porous medium equation. Comm. Partial Differential Equations 26:1–2 (2001), 101–174.
    • (2001) Comm. Partial Differential Equations , vol.26 , Issue.1-2 , pp. 101-174
    • Otto, F.1
  • 27
    • 0001559554 scopus 로고    scopus 로고
    • Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
    • Otto, Felix, Villani, Cedric, Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173:2 (2000), 361–400.
    • (2000) J. Funct. Anal. , vol.173 , Issue.2 , pp. 361-400
    • Otto, F.1    Villani, C.2
  • 28
    • 84881613408 scopus 로고    scopus 로고
    • On the planning problem for a class of mean field games
    • Porretta, Alessio, On the planning problem for a class of mean field games. C. R. Math. Acad. Sci. Paris 351:11–12 (2013), 457–462.
    • (2013) C. R. Math. Acad. Sci. Paris , vol.351 , Issue.11-12 , pp. 457-462
    • Porretta, A.1
  • 29
    • 84899459829 scopus 로고    scopus 로고
    • On the planning problem for the mean field games system
    • Porretta, Alessio, On the planning problem for the mean field games system. Dyn. Games Appl. 4:2 (2014), 231–256.
    • (2014) Dyn. Games Appl. , vol.4 , Issue.2 , pp. 231-256
    • Porretta, A.1
  • 30
    • 85049485297 scopus 로고    scopus 로고
    • Weighted Energy-Dissipation principle for gradient flows in metric spaces
    • in press
    • Rossi, Riccarda, Savaré, Giuseppe, Segatti, Antonio, Stefanelli, Ulisse, Weighted Energy-Dissipation principle for gradient flows in metric spaces. J. Math. Pures Appl., 2018, 10.1016/j.matpur.2018.06.022 in press.
    • (2018) J. Math. Pures Appl.
    • Rossi, R.1    Savaré, G.2    Segatti, A.3    Stefanelli, U.4
  • 31
    • 0012712796 scopus 로고    scopus 로고
    • Minimax and Monotonicity
    • Springer-Verlag Berlin
    • Simons, Stephen, Minimax and Monotonicity. Lecture Notes in Mathematics, vol. 1693, 1998, Springer-Verlag, Berlin.
    • (1998) Lecture Notes in Mathematics , vol.1693
    • Simons, S.1
  • 32
    • 37349070894 scopus 로고    scopus 로고
    • Optimal Transport: Old and New
    • Fundamental Principles of Mathematical Sciences Springer-Verlag Berlin
    • Villani, Cédric, Optimal Transport: Old and New. Grundlehren der Mathematischen Wissenschaften (Trans.) Fundamental Principles of Mathematical Sciences, vol. 338, 2009, Springer-Verlag, Berlin.
    • (2009) Grundlehren der Mathematischen Wissenschaften , vol.338
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.