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
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
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
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
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 Mbodj) "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 (with Larry Karp and Rashid Sumaila), "Equilibrium management of fisheries with
altruistic ovelapping generations", working paper [pdf]
147 "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]
148. (with Alfred Galichon) "Pareto indivisible allocations, revealed preferences and duality", working paper, January 2012 [pdf]
149. (with Qinlong Zhou and Yiming Long), "Economic growth and sustainable
development: how should we discount the future? " working paper,
May 2012 [pdf]
150. (with Walter Schachermayer), "Optimal
transport and the geometry of L1(Rd)", working paper,, May 2012 [pdf]