Duality for the level sum of quasiconvex functions and applications
ESAIM: Control, Optimisation and Calculus of Variations, Tome 3 (1998), pp. 329-343.
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     author = {Volle, M.},
     title = {Duality for the level sum of quasiconvex functions and applications},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {329--343},
     publisher = {EDP-Sciences},
     volume = {3},
     year = {1998},
     zbl = {0904.49023},
     mrnumber = {1641843},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_1998__3__329_0/}
}
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Volle, M. Duality for the level sum of quasiconvex functions and applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 3 (1998), pp. 329-343. http://archive.numdam.org/item/COCV_1998__3__329_0/

[1] C. Amara: Directions de majoration d'une fonction quasiconvexe et applications, Serdica Math. J., 23, 1997, 1001-1018. | Zbl 1030.90087

[2] H. Attouch, R. Wets: Epigraphical analysis, in Analyse non linéaire, H. Attouch, J.-P. Aubin, F. Clarke, I. Ekeland eds., Gauthier-Villars, Paris, 1989, 73-100. | Numdam | MR 1019109 | Zbl 0676.49003

[3] H. Attouch, M. Volle: Cutting and scanning methods in set-valued analysis, Set-Valued Analysis, 4, 1996, 135-155. | MR 1394410 | Zbl 0849.41028

[4]M. Avriel, W. Diewert, S. Schaible, I. Zang: Generalized concavity, Plenum Press, New York, 1987. | MR 927084 | Zbl 0679.90029

[5] F. Baccelli, G. Cohen, G.J. Olsder, J.-P. Quadrat: Synchronization and linearity: an algebra for discrete event Systems, John Wiley and Sons, New York 1992. | MR 1204266 | Zbl 0824.93003

[6] G. Barles: Solutions de viscosité des équations de Hamilton-Jacobi, Math. et Appl. 17, Springer-Verlag, 1994. | MR 1613876 | Zbl 0819.35002

[7] E. N. Barron, R. Jensen, W. Liu: Hopf-Lax-Type Formula for ut + H(u, Du) = 0, J. Diff. Eq., 126, 1996, 48-61. | MR 1382056 | Zbl 0857.35023

[8] E.N. Barron, W. Liu: Calculus of variations in L∞, Appl. Math. Optim., 35, 1997, 237-263. | MR 1431800 | Zbl 0871.49017

[9] G. Birkhoff: Lattice Theory, Providence, A.M.S., 1966. | MR 227053 | Zbl 0153.02501

[10] M.G. Crandall, P.-L. Lions: Viscosity solutions of Hamilton Jacobi equations, Trans. Amer. Math. Soc., 277, 1983, 1-42. | MR 690039 | Zbl 0599.35024

[11] J.-P. Crouzeix: Polaires quasiconvexes et dualite, C. R. Acad. Sci. Paris, 297, Série A, 1974, 955-958. | MR 365302 | Zbl 0303.90047

[12] J.-P. Crouzeix: Deux notions de polarité pour les fonctions quasiconvexes, C. R. Acad. Sci. Paris, 282, Série A, 1976, 107-109. | MR 399382 | Zbl 0353.90079

[13] J.-P. Crouzeix: Contributions à l'étude des fonctions quasiconvexes, Thesis, University of Clermont-Ferrand II, France, 1977. | MR 484417

[14] L.C. Evans: Some min-max methods for the Hamilton-Jacobi equation, Ind. Math. J., 33-1, 1984, 31-50. | MR 726105 | Zbl 0543.35012

[15] W. Fenchel: Convex cones, sets and functions, University of Princeton, 1953. | Zbl 0053.12203

[16] M. Gondran: Analyse minimax, C. R. Acad. Sci. Paris, 323, Série I, 1996, 1249-1252. | MR 1428545 | Zbl 0877.49012

[17] L. Hörmander: Sur la fonction d'appui des ensembles convexes dans un espace localement convexe, Ark. Mat., 3, 1954, 181-186. | MR 68112 | Zbl 0064.10504

[18] D.T. Luc, M. Volle: Level set under infimal convolution and level addition, J.O.T.A., 94-3, 1997, 695-714. | MR 1470889 | Zbl 0892.90179

[19] J.E. Martinez-Legaz: Quasiconvex duality theory by generalized conjugations methods, Optimization. 19, 1988, 603-652. | MR 960433 | Zbl 0671.49015

[20] J.E. Martinez-Legaz, I. Singer: V-Dualities and ⊥-dualities, Optimization, 22-4, 1991, 483-511. | MR 1106537 | Zbl 0728.06007

[21] J.-J. Moreau: Inf-convolution, sous-additivité, convexité des fonctions numériques, J. Math. Pures Appl., 49, 1970, 109-154. | MR 288602 | Zbl 0195.49502

[22] J.-P. Penot: Starshaped functions and conjugacy, Preprint, University of Pau, France, 1996.

[23] J.-P. Penot, M. Volle: Another duality scheme for quasiconvex problems, International Series of Numerical Math., 84, 1988, Birkaüser Verlag Basel, 259-275. | MR 1017957 | Zbl 0662.49009

[24] J.-P. Penot, M. Volle: Inversion of real-valued functions and applications, ZOR Methods and Models of Operations Research, 34, 1990, 117-141. | MR 1045821 | Zbl 0718.49012

[25] J.-P. Penot, M. Volle: On quasiconvex duality, Math. Oper. Res., 15-4, 1990, 597-625. | MR 1080468 | Zbl 0717.90058

[26] P. Plazanet: Contributions à l'analyse des fonctions convexes et des différences de fonctions convexes. Application à l'optimisation et à la théorie des e.d.p., Thesis, University Paul Sabatier, Toulouse, France, 1990.

[27] R.T. Rockafellar: Duality theorems for convex functions, Bull. Amer. Math. Soc., 70, 1964, 189-192. | MR 165429 | Zbl 0121.14803

[28] R.T. Rockafellar: Convex Analysis, Princeton, 1970. | MR 274683 | Zbl 0193.18401

[29] A.M. Rubinov, B.M. Glower: On generalized quasiconvex conjugation, Contemp. Math., 204, 1997, 199-216. | MR 1443004 | Zbl 0876.90076

[30] A. Seeger, M. Volle: On a convolution operation obtained by adding level sets: classical and new resuits, Operations Research, 29-2, 1995, 131-154. | Numdam | MR 1337887 | Zbl 0835.90094

[31] I. Singer: The lower semicontinuous quasiconvex hull as a normalized second conjugate, Nonlinear Anal. Theory Methods Appl., 7, 1983, 1115-1121. | MR 719363 | Zbl 0528.49007

[32] P.T. Thach: A nonconvex duality with a zero duality gap and applications, SIAM J. Optim., 4, 1994, 44-64. | MR 1260406 | Zbl 0999.49503

[33] S. Traoré, M. Volle: On the level sum of two convex functions on Banach spaces, Journal of Convex Analysis, Part II of the Special Issues in Honor of R.T. Rockafellar, 3-1, 1996, 141-151. | MR 1422757 | Zbl 0876.49011

[34] M. Volle: Conjugaison par tranches, Ann. Mat. Pura ed Appl., 139, 1985, 279-311. | MR 798177 | Zbl 0581.49007

[35] M. Volle: Quasiconvex duality for the max of two functions, Lecture Notes in Economics and Math. Systems, 452, 1997, 365-379. | MR 1467042 | Zbl 0921.49027

[36] M. Volle: Conditions initiales quasiconvexes dans les équations de Hamilton-Jacobi, C. R. Acad. Sci. Paris, 325, Série I, 1997, 167-170. | MR 1467071 | Zbl 0913.70013