Publications by Ivar Ekeland:
Chronological order



1.  "Désintégration des mesures vectorielles", Note CRAS Paris, 266 (1968), p.816-819.

2.  "Paramétrisation en théorie de la commande",  Note CRAS Paris, 267 (1968), p.98-100

3.  "Existence de solutions optimales pour des problèmes de contrôle de systèmes gouvernés par des équations différentielles ordinaires", Cahiers de l'IRIA, 1 (1969), p.41-78.


4.  "Sur certains problèmes de contrôle optimal"Note CRAS Paris, 268 (1969), p.1585-1588


5.  "Suites minimisantes et solutions de certains problèmes de contrôle optimal", Symposium on Optimization, Springer Lecture Notes in Mathematics 132 (1970), p.79-84


6.  "Relaxation de problèmes de contrôle pour des systèmes décrits par des équations aux dérivées partielles", Note CRAS Paris 270 (1970), p. 1283-1286.


7.  "Formes équivalentes d'un problème relaxé", Note CRAS Paris 271 (1970), p.289-292.


8. (with M. Valadier) "Representation of set-valued mappings"J. Math. An. and App. 35 (1971), p.621-629.


9. "Sur le contrôle optimal de systèmes gouvernés par des équations elliptiques", J. Funct. An. 29 (1972), p.1-62.


10. "Quelques applications de l'analyse convexe à la résolution de problèmes d'optimisation non convexes", Analyse Convexe et ses Applications, Springer Lecture Notes in Economics and Mathematical Systems 102 (1974), p.102-114


11. "Une estimation a priori en programmation non convexe", Note CRAS Paris 279 (1974), p.149-151


12.  "Topologie différentielle et théorie des jeux"Topology 13 (1974), p.375-388. 


13. (avec J.P. Aubin) "Minimisation de critères intégraux", Note CRAS Paris 281 (1975), p.285-288.



14. "Some general properties of non-cooperative games", Control Theory, Numerical Methods and Computer Systems Modelling, Springer Lecture Notes in Economics and Mathematical Systems 107 (1975) p.134-139


15. (avec J.P. Aubin) "Estimates of the duality gap in non-convex optimization problems", Math. of Operations Research 1 (1976) p.225-245

16. (avec J.M. Lasry) "Sur le nombre de points critiques de fonctions invariantes par des groupes"Note CRAS Paris 282 (1976), p.559-562


17. (avec H. Brézis) "Un principe variationnel associé à certaines équations paraboliques. Le cas indépendant du temps", Note CRAS Paris 282 (1976), p.971-975


18. (avec H. Brézis) "Un principe variationnel associé à certaines équations paraboliques. Le cas dépendant du temps", Note CRAS Paris 282 (1976), p.1197-1198


19.
"Legendre duality in non-convex optimization and calculus of variations", SIAM J. Opt. and Control 15 (1977), p.905-934 


20. "Discontinuités de champs hamiltoniens et existence de solutions optimales pour des problèmes de calcul des variations", Publications Mathématiques de l'IHES 47 (1977), p.5-32 


21. (avec F. Clarke) "Solutions périodiques, de période donnée, des équations hamiltoniennes", Note CRAS Paris 287 (1978), p.1013-1015


22. Review of "Convex analysis and measurable multifunctions" by Castaing and Valadier, Bull. AMS 84 (1978), p.950-956


23. "Nonconvex duality", Analyse non convexe, Mémoires de la SMF 60 (1979), p.45-55


24. "Possibilités offertes par la théorie du contrôle pour l'identification d'un modèle présentant le meilleur pouvoir prédictif", Elaboration et Justification des Modèles, Maloine, 1979


25. "Periodic solutions to Hamiltonian equations and a theorem of P. Rabinowitz", J. Diff. Eq. 34 (1979), p.523-534


26. (avec J.M. Lasry) "Nombre de solutions périodiques des équations de Hamilton", Note CRAS Paris 288 (1979), p.209-211


27. (avec F. Clarke) "Oscillations entretenues de systèmes hamiltoniens non linéaires", Note CRAS Paris 289 (1979), p.393-395


28. (avec P. Bates) "A saddle-point theorem", Differential Equations, Ahmad, Keene and Lazer ed., Academic Press, 1980


29.  (avec J.P. Aubin) "Second-order equations with convex Hamiltonian", Canadian Math. Bull. 23 (1980), p.81-94


30. (avec J.M. Lasry) "Principes variationnels en dualité", Note CRAS Paris 291 (1980), p.493-497

31.  (avec J.P. Aubin) "Second-order equations with convex Hamiltonian", Canadian Math. Bull. 23 (1980), p.81-94 


32. (avec F. Clarke) "Hamiltonian trajectories having prescribed minimal period", Comm. Pure App. Math. 33 (1980), p.103-116


33. (avec J.M. Lasry) "On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface", Annals of Math.112 (1980), p.283-319


34. "Solutions périodiques des équations de Hamilton", in Nonlinear Partial Differential Equations and their Applications 1 (1980), Brézis and Lions ed., Pitnam, 1980


35. "Forced oscillations for nonlinear Hamiltonian systems II", Advances in Mathematics, volume in honour of L. Schwartz, Nachbin ed., Academic Press, 1981

36. "Oscillations de systèmes hamiltoniens non linéaires III", Bull. SMF, 109 (1981), p.297-330


37. "Dualité et stabilité des systèmes hamiltoniens", CRAS Paris 294 (1982), p.673-676


38. (avec F. Clarke) "Nonlinear oscillations and boundary-value problems for Hamiltonian systems", Arch. Rat. Mech. and An. 78 (1982), p.315-333


39. (avec J.M. Lasry) "Duality in non-convex variational problems", Advances in Hamiltonian Systems, Aubin, Bensoussan and Ekeland ed., (1983), Birkhaüser-Boston



40. "A perturbation theory near convex Hamiltonian systems", J. Diff. Eq. 50 (1983), p.407-440



41. "Dual variational methods in non-convex optimization and differential equations", Mathematical Theories of Optimization, Cecconi and Zolezzi ed., Springer Lecture Notes in Mathematics 979 (1983) p.108-120



45. (avec J.M. Lasry) "Duality in non-convex variational problems", Advances in Hamiltonian Systems, Aubin, Bensoussan and Ekeland ed., (1983), Birkhaüser-Boston

46 "Dual variational methods in non-convex optimization and differential equations", Mathematical Theories of Optimization, Cecconi and Zolezzi ed., Springer Lecture Notes in Mathematics 979 (1983) p.108-120


47. "A Morse theory for Hamiltonian systems", Differential Equations, Knowles and Lewis ed., North-Holland (1984), p.165-172


48. "Une théorie de Morse pour les systèmes hamiltoniens convexes", Annales IHP "Analyse non linéaire" 1 (1984), p.19-78


49. "Hypersurfaces pincées et systèmes hamiltoniens", Note CRAS Paris 299 (1984), p.669-672



50. "Periodic solutions of convex Hamiltonian sysems: the index and its use", Nonlinear oscillations for conservative systems, Ambrosetti ed., Pitagora editrice, 1985


51. (avec L. Lassoued) "Un flot Hamiltonien a au moins deux trajectoires fermées sur toute surface d'énergie convexe et bornée", Note CRAS Paris 301 (1985), p.162-164

52. (with H. Hofer) "Periodic solutions with prescribed period for convex autonomous Hamiltonian systems", Inventiones Math 81 (1985), p. 155-188 


53. "An index theory for periodic solutions of convex Hamiltonian systems", Nonlinear Functional Analysis and its Applications, F. Browder editor, Proceedings of Symposia in Pure Mathematics 45 (1986), p. 395-423


54. "Some complements of convex analysis", Optimization and related fields , Lecture Notes in Mathematics 1190 (1986), p. 215-229


55. "Some variational problems arising from mathematical economics", Mathematical Economics, CIME Lectures 1986, Ambrosetti, Gori and Luchetti ed., Springer, Lecture Notes in Mathematics n°1330


56. (with A. Ambrosetti and C. Coti Zelati) "Symmetry breaking in critical point theory and applications" J. Diff. Eq. 67 (1987), p.165-184


57. (avec L. Lassoued) "Multiplicité des trajectoires fermées d'un système Hamiltonien sur une hypersurface d'énergie convexe", Annales IHP "Analyse non linéaire" 4 (1987) p.1-29


58 (avec H. Hofer) "Subharmonics of convex non-autonomous Hamiltonian systems", Comm. Pure and Applied Math 40 (1987), p. 1-37


59. (avec H. Hofer), "Sur les hypersurface convexes et leurs caractéristiques fermées", Note CRAS Paris, 304 (1987), p. 237-240


60. (avec H. Hofer) "Convex Hamiltonian energy surfaces and their closed trajectories", Comm Math. Physics 113 (1987) p.419-467 


61. "Variational methods", p. 5041-5047, Systems and Control Encyclopedia, Madan Singh editor , Pergamon Press, 1987


62. "The calculus of variations: from minimization problems to critical point theory", Contributions to modern calculus of variations, Cesari editor, p. 91-101, Pitman Research Notes, Longman, 1987


63 (with H. Hofer) "Capacités symplectiques", Note CRAS Paris, 307 (1988), p.37-40


64. "The mountain-pass theorem and some applications", Minimax results of Liusternik-Schnirelman type and applications, Séminaire de Mathématiques Supérieures, Université de Montréal, 1989


65. (with H. Hofer) "Two symplectic fixed-point theorems with applications to Hamiltonian dynamics", J. Math. Pures et App. 68 (1989), p.467-489


66. (with H. Hofer) "Symplectic topology and Hamiltonian dynamics", Zeitschrift für Mathematik 200 (1989) p.355-378


67. (with A. Ambrosetti), "Perturbation results for a class of singular Hamiltonian systems", Rendiconti dell'Academia dei Lincei, (8), 83 (1989), pp. 129-132


68. (with B.M. d'Onofrio), "Hamiltonian systems with elliptic periodic orbits", Nonlinear Analysis TMA 14 (1990) p. 11-21


69. (with B.M. D'Onofrio) "Morse theory and the existence of periodic solutions of elliptic type", in Variational methods", Berestycki, Ekeland and Coron ed. , Birkhaüser, Progress in Nonlinear Differential Equations and their Applications, 1990, p. 447-454


70. (with V. Coti Zelati and Eric Séré), "Solutions doublement asymptotiques de systèmes hamiltoniens convexes", Note CRAS Paris 310 (1990) p. 631-633


71. (with V. Coti Zelati and Eric Séré), " A variational approach to homoclinic orbits in Hamiltonian systems", Mathematische Annalen (1990) p. 133-160


72. (with A. Ambrosetti), "Periodic solutions of a class of singular Hamiltonian systems", Proc. Royal Soc. Edinburgh 114 A(1990), p.1-13 (volume in honor of Jack Hale)


73. (with H. Hofer) "Symplectic topology and Hamiltonian dynamics II", Mathematische Zeitschrift, 203 (1990) p. 553-567


74. "Les solutions périodiques en mécanique analytique", Actes du Colloque sur la "Mécanique Analytique" de Lagrange et son héritage, Paris, 27-29 Septembre1989, fondation Hugot du Collége de France; Atti della Accademia delle Scienze di Torino 124 (1990) , supplemento, p.159-167


80 (with V. Coti Zelati and P.L. Lions) "Index estimates and critical points of functionals not satisfying Palais-Smale" , Annali della Scuola Normale Superiore di Pisa, Scienze Fisiche e Matematiche, Serie IV Vol XVII Fasc.4 (1990) p. 569-582


90.  (with S. Mathlouti) "Calcul numérique de la capacité symplectique", Progress in Variational Methods in Hamiltonian systems and elliptic equations, Wiley, Pitman Research Notes in Math., Ser 243, p. 68-91 (1992)


91. (with G.F. Dell'Antonio and B.M. D'Onofrio) "Les systèmes hamiltoniens convexes et pairs ne sont pas ergodiques en général", CRAS Paris, 315 (1992) p. 1413-1415


92 (with P. Courty, J.M. Morel and Cheuk Wai Yip) "Linéarisation du problème de l’adossement financier sur des bases d’ondeletes", CRAS Paris, 316 (1993) p. 1341-1344


93  "Finance: un nouveau domaine des mathématiques appliquées", Revue Française de Gestion, 96 (1993), p.44-48


94. (with G.F. Dell'Antonio and B.M. D'Onofrio) "Stability from index estimates for periodic solutions of Hamiltonian systems", J. Diff. Eq, 108 (1994) p. 170-189


95.  (with G.F. Dell'Antonio and B.M. D'Onofrio) "Nonergodic properties of systems of oscillators coupled through convex even potentials", Variational methods in nonlinear analysis, p. 77-83, A. Ambrosetti and K.C. Chang ed. , Gordon and Breach, 1995

96. (with G.F. Dell'Antonio and B.M. D'Onofrio) "Periodic solutions of elliptic type for strongly nonlinear Hamiltonian systems", Floer memorial volume, Birkhauser, 1995, p. 327-335


97  (with N. Ghoussoub and H. Tehrani) "Multiple solutions for a classical problem in the calculus of variations", J. Diff.Equ. 131 (1996), p. 229-243


98 (with P.A.Chiappori) "Problèmes d'agrégation en théorie du consommateur et calcul différentiel extérieur", C.R.A.S Paris 323 (1996), p. 565-570


99 " Finance et modélisation", Encyclopédie des Marchés Financiers, Y. Simon ed., Economica, 1997, p. 485-500



100 "Quelques modèles mathématiques de la peréquation tarifaire", Economie et Société, Cahiers de l'ISMEA, 31, n° 5-6 (1997), p.223-233

101  (with P.A. Chiappori) "A convex Darboux theorem", Annali della Scuola Normale Superiore di Pisa Cl. Sci. (4) (volume en l'honneur de E. De Giorgi), 25 (1997), p. 287-297


102  (with N. Ghoussoub) "Equivariant Liusternik-Schnirelman theory for non-even functionals", Annales de l'IHP, Analyse non linéaire 15 (1998) p 341-370


103. (with P.A. Chiappori), "Disaggregation of collective excess demand functions in incomplete markets", J. Mathematical Economics, 31 (1998), p. 111-130; see also "Corrigendum" to the preceding, same journal, 33 (2000), p. 531-532


104 (with P. A. Chiappori) "Aggregation and market demand: an exterior differential calculus viewpoint", Econometrica, 67 (1999), p. 1435-1458


105 "Testable consequences of economic theory", Decisions in Economics and Finance 23 (1) 2000, p.1-13


106 "Mathematical models in economics", Proceedings of the International Conference on the Mathematical Sciences after the year 2000, Khalil bitar, Ali Chamseddine and Wafic Sabra editors, World Scientific, 2000 (ISBN 981-02-4223-9)


107  (with N. Ghoussoub) "Selected new aspects of the calculus of variations in the large", Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 2, p.207-265

108 (with P.A. Chiappori. F. Kubler and H. Polemarchakis). "The identification of preferences from equilibrium prices: uncertainty", Journal of Economic Theory 102 (2002), p. 403-420 

109. (with L. Nirenberg) "A convex Darboux theorem", Methods and applications of analysis 9 (2002), p. 329-344

110"Two Problems in Economics", Jahresbericht der DMV, 104 (2002), p. 52-58


111. (with J.Heckman and L.Nesheim) "Identifying hedonic models", in "Market implications of peer and neighbourhood effects", American Economic Association papers and proceedings, vol 92 (2002), 2, p. 304-309

112.  "Some applications of the Cartan-Kähler theorem to economic theory". Erich Kähler: Mathematische Werke / Mathematical Works. 767 - 777 de Gruyter, book editors: Berndt, Rudolf and Oswald Riemenschneider. Berlin. 2003

113. (with Pierre-Andre Chiappori, Felix Kubler and Herakles Polemarchakis): "Testable implications of general equilibrium theory: a differentiable approach" Journal of Mathematical Economics, 40 (2004) p. 105-119

114. (with Pierre-Andre Chiappori): "Individual excess demands" Journal of Mathematical Economics, 40 (2004) p. 41-57

115. (with Pierre-Andre Chiappori): "Applying exterior differential calculus to economics: a presentation and some new results". Japan and the World Economy. 16 .3. (August 2004). pp. 363 - 385



116 (with Bruno Bouchard and Nizar Touzi): "On the Malliavin approach to Monte-Carlo approximation of conditional expectations" Finance and Stochastics, 1 (2004), p.1-29


117 . (with Guillaume Carlier) "The structure of cities, J. Global Optimization 4 (2004), p. 371-376

118. (with Jim Heckman and Lars Nesheim): "Identification and estimation of hedonic models" Journal of Political Economy 112 (2004) p.60-109

119. "An optimal matching problem". ESAIM-Control, Optimization and Calculus of Variations, 11 (2005) p. 57-71 


120  (with Erik Taflin) “A theory of bond portfolios” Annals of Applied Probability. 15 (2005) p. 1260 - 1305.

 

121  (with Louis Nirenberg). "Regularity in an unusual variational problem”,  Journal of Mathematical Fluid Mechanics 7, Supplement 3 (2005) p. 332 -348



122. "A duality theory for non-convex functions of matrices", Ricerche di Matematica 55 (2006) p. 1-12 


123. (with Ngalla Djitte) "An inverse problem in the economic theory of demand", Annales de l’IHP – Analyse non lineaire. 23 (2006) p. 269 - 281.

123. (with Pierre-André Chiappori) "The microeconomics of group behaviour: general characterization", Journal of Economic Theory 130 (2006): p.1 – 26 


124 (with Ali Lazrak), "Being serious about non-commitment: subgame perfect equilibria in continuous time" ArXiv (April 2006)
arXiv:math/0604264


125 (with Guillaume Carlier) "Equilibrium structure of an bidimensional assymmetric city". Nonlinear Analysis : Real World Applications 8 (2007) p.725 - 748.

126. (with Erik Taflin) “Optimal Bond Portfolios”, Paris-Princeton Lectures in Mathematical Finance, vol 3, Lecture Notes in Mathematics, Springer (2007), p.1-48 

127  (with Guillaume Carlier and Nizar Touzi "Optimal derivatives design for mean-variance agents under adverse selection". Mathematics and Financial Economics. 1 (2007) p. 57 - 80.



128. (with Martin Browning and Pierre-André Chiappori) "Local disaggregation of negative demand and excess demand functions", Journal of Mathematical Economics 43 (2007).764 - 770.


129. (with Ali Lazrak) "Equilibrium policies when preferences are time inconsistent" ArXiv (Aug 2008) arXiv:0808.3790

130. (with Traian  Pirvu) "Investment and consumption without commitment" Mathematics and Financial Economics. 2 (2008) p. 57 - 86.


131 "Discounting the future: the case of climate change", Cahiers de la Chaire Finance et Développement Durable 27 (2009), Université Paris-Dauphine


132 (with Rashid Sumaila and Claudio Pareja) "Sustainable fisheries management", working paper, Cahiers de la Chaire Finance et Développement Durable 17 (2009), Université Paris-Dauphine


133.
(with Pierre-André Chiappori) "The microeconomics of efficient group behavior: identification"  Econometrica  77 (2009), p.  763–799.


134 (with Roger Guesnerie) "Factor price equalization and the geometry of global production”, Journal of Mathematical Economics 46 (2010) p. 666–690 (pdf)

135. "From Frank Ramsey to René Thom: a classical problem in the calculus of variations leading to an implicit differential equation", Discrete and Contunuous Dynamical Systems, 28, 3 (2010) p. 1101 - 1119 (pdf)

136 (with Ali Lazrak) "The golden rule when preferences are time-inconsistent", Mathematics and Financial Economics. 2 (2008) p. 57 - 86. 4 (2010) p. 29-55 (pdf)


137. "Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types" Economic Theory 42 (2010) p.  275–315 (pdf)
 

138.  (with Guillaume Carlier) “Matching for teams” Economic Theory 42 (2010) p. 397 - 418 (pdf)


139. (with Alfred Galichon and Marc Henry) "Optimal transportation and the falsifiability of incompletely specified economic models",  Economic Theory   42 (2010) p. 355 - 374  (pdf)


140. (with Santiago Moreno-Bromberg) "An algorithm for computing solutions of variational problems with global convexity constraints". Numerische Mathematik 115 (2010) p. 45-69 [pdf]


141. (with Alfred Galichon and Marc Henry) "Comonotonic measures of multivariate risk", Mathematical Finance, 20 (2010) p. 1-24  [pdf]


142. (with Pierre-André Chiappori) "New developments in aggregation economics", Annual Review of Economics,  3 (2011) p. 631-668

143. (with Elliott Norse, Sandra Brooke, William Cheung, Malcolm Clark, Rainer Froese, Kristina Gjerde, Richard Haedrich, Sel9ina Heppell, Telmo Morato, Lance Morgan, Daniel Pauly, Rashid Sumaila, Reg Watson), "Sustainability of deep-sea fisheries", Marine Policy 36 (2012) p. 307-320  [pdf]


144. (with Traian  Pirvu and Oumar Mbodji) "Time consistent portfolio management" SIAM Journal of Financial Mathematics  3 (2012) p. 1-32  (pdf)


145  (with Walter Schachermayer) "Law invariant risk measures in L\infty(Rd)", Statistics and Risk Modeling, Vol. 28 (2011), No. 3, pp. 195-225.[pdf]


146 "Les enjeux économiques du développement durable: le cas des pêcheries", Annales d'Économie et de Statistiques, Hors Série 1 (2012), "Économie, environnement et destin des générations futures" [pdf]

147. (with Alfred Galichon) "The housing problem and revealed preference theory: duality and an application", (2012),  Economic Theory, 54 (2013) p. 425-441  [pdf]


148. (with Walter Schachermayer), "Optimal transport and the geometry of
L1(Rd)" (2012)  Proceedings of the AMS, Vol. 142 (2014), pp. 3585-3596  [pdf]


149. (with Qinlong Zhou and Yiming Long), "A new class of problems in the calculus of variations ", Regular and Chaotic Dynamics,   p. 553-584  [pdf]

150.
(with Marwan Aloqeili and Guillaume Carlier), "Restrictions and identification in a multidimensional risk-sharing problem", Economic Theory, 56 (June 2014), p.409-423 [pdf]4


151. (with E. Séré)  "An implicit function theorem for non-smooth maps between Fréchet spaces",   https://arxiv.org/abs/1502.01561  March 2014 (see here for a version with figures)

152. (with Larry  Karp and Rashid  Sumaila) "Equilibrium resource management with altruistic overlapping generations". Journal of Environmental Economics and Management, Volume 70, March 2015, p. 1-16 [pdf]


153. "How to build stable relationships between people who lie and cheat", Milan Journal of Mathematics, 82 (2014), p. 67-79 [pdf]


154. (with Maurice Queyranne) "Optimal pits and optimal transportation", ESAIM Mathematical Modeling and Numerical Analysis, Optimal pits and optimal transportation (2015) DOI: 10.1051/m2an/2015026 [pdf]


155.
(with Geir Asheim) "Resource conservation across generations in a Ramsey-Chichilnisky game", Economic Theory (2015) 61(4) p, 611-639 [pdf]


156. (with Juan Carluccio and Roger Guesnerie) "Fragmentation and wage inequality: insights from a simple model", March 2017, Annals of Economics and Statistics, special issue in honor of Edmond Malinvaud, 125/126 (June 2017), p. 113-134 [pdf]


157 "Hamilton-Jacobi on the symplectic group", March 2017, Rendiconti dell'Istituto di Matematica dell'Università di Trieste, special issue dedicated to Jean Mawhin, to appear [pdf]

158. "Nash", Milan Journal of Mathematics, 85 (2017), p. 1-11 [pdf]


159. "On the Euler-Lagrange equation in the calculus of variations" Vietnam Journal of Mathematics, 46(1), March 2018, p. 1-5 [pdf]


160. (with Delphine Lautier and Bertrand Villeneuve) "Hedging pressure and speculation in commodity markets" , to appear, Economic Theory, [pdf]


161. (with Guillaume Carlier), "Equilibrium in quality markets: beyond the transferable case", to appear, Economic Theory, 2018, [pdf]


   

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