@article{COCV_1998__3__329_0, 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}, mrnumber = {1641843}, zbl = {0904.49023}, language = {en}, url = {http://www.numdam.org/item/COCV_1998__3__329_0/} }
TY - JOUR AU - Volle, M. TI - Duality for the level sum of quasiconvex functions and applications JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1998 SP - 329 EP - 343 VL - 3 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_1998__3__329_0/ LA - en ID - COCV_1998__3__329_0 ER -
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://www.numdam.org/item/COCV_1998__3__329_0/
[1] Directions de majoration d'une fonction quasiconvexe et applications, Serdica Math. J., 23, 1997, 1001-1018. | Zbl
:[2] Epigraphical analysis, in Analyse non linéaire, H. Attouch, J.-P. Aubin, F. Clarke, I. Ekeland eds., Gauthier-Villars, Paris, 1989, 73-100. | Numdam | MR | Zbl
, :[3] Cutting and scanning methods in set-valued analysis, Set-Valued Analysis, 4, 1996, 135-155. | MR | Zbl
, :[4]Generalized concavity, Plenum Press, New York, 1987. | MR | Zbl
, , , :[5] Synchronization and linearity: an algebra for discrete event Systems, John Wiley and Sons, New York 1992. | MR | Zbl
, , , :[6] Solutions de viscosité des équations de Hamilton-Jacobi, Math. et Appl. 17, Springer-Verlag, 1994. | MR | Zbl
:[7] Hopf-Lax-Type Formula for ut + H(u, Du) = 0, J. Diff. Eq., 126, 1996, 48-61. | MR | Zbl
, , :[8] Calculus of variations in L∞, Appl. Math. Optim., 35, 1997, 237-263. | MR | Zbl
, :[9] Lattice Theory, Providence, A.M.S., 1966. | MR | Zbl
:[10] Viscosity solutions of Hamilton Jacobi equations, Trans. Amer. Math. Soc., 277, 1983, 1-42. | MR | Zbl
, :[11] Polaires quasiconvexes et dualite, C. R. Acad. Sci. Paris, 297, Série A, 1974, 955-958. | MR | Zbl
:[12] Deux notions de polarité pour les fonctions quasiconvexes, C. R. Acad. Sci. Paris, 282, Série A, 1976, 107-109. | MR | Zbl
:[13] Contributions à l'étude des fonctions quasiconvexes, Thesis, University of Clermont-Ferrand II, France, 1977. | MR
:[14] Some min-max methods for the Hamilton-Jacobi equation, Ind. Math. J., 33-1, 1984, 31-50. | MR | Zbl
:[15] Convex cones, sets and functions, University of Princeton, 1953. | Zbl
:[16] Analyse minimax, C. R. Acad. Sci. Paris, 323, Série I, 1996, 1249-1252. | MR | Zbl
:[17] Sur la fonction d'appui des ensembles convexes dans un espace localement convexe, Ark. Mat., 3, 1954, 181-186. | MR | Zbl
:[18] Level set under infimal convolution and level addition, J.O.T.A., 94-3, 1997, 695-714. | MR | Zbl
, :[19] Quasiconvex duality theory by generalized conjugations methods, Optimization. 19, 1988, 603-652. | MR | Zbl
:[20] V-Dualities and ⊥-dualities, Optimization, 22-4, 1991, 483-511. | MR | Zbl
, :[21] Inf-convolution, sous-additivité, convexité des fonctions numériques, J. Math. Pures Appl., 49, 1970, 109-154. | MR | Zbl
:[22] Starshaped functions and conjugacy, Preprint, University of Pau, France, 1996.
:[23] Another duality scheme for quasiconvex problems, International Series of Numerical Math., 84, 1988, Birkaüser Verlag Basel, 259-275. | MR | Zbl
, :[24] Inversion of real-valued functions and applications, ZOR Methods and Models of Operations Research, 34, 1990, 117-141. | MR | Zbl
, :[25] On quasiconvex duality, Math. Oper. Res., 15-4, 1990, 597-625. | MR | Zbl
, :[26] 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] Duality theorems for convex functions, Bull. Amer. Math. Soc., 70, 1964, 189-192. | MR | Zbl
:[28] Convex Analysis, Princeton, 1970. | MR | Zbl
:[29] On generalized quasiconvex conjugation, Contemp. Math., 204, 1997, 199-216. | MR | Zbl
, :[30] On a convolution operation obtained by adding level sets: classical and new resuits, Operations Research, 29-2, 1995, 131-154. | Numdam | MR | Zbl
, :[31] The lower semicontinuous quasiconvex hull as a normalized second conjugate, Nonlinear Anal. Theory Methods Appl., 7, 1983, 1115-1121. | MR | Zbl
:[32] A nonconvex duality with a zero duality gap and applications, SIAM J. Optim., 4, 1994, 44-64. | MR | Zbl
:[33] 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 | Zbl
, :[34] Conjugaison par tranches, Ann. Mat. Pura ed Appl., 139, 1985, 279-311. | MR | Zbl
:[35] Quasiconvex duality for the max of two functions, Lecture Notes in Economics and Math. Systems, 452, 1997, 365-379. | MR | Zbl
:[36] Conditions initiales quasiconvexes dans les équations de Hamilton-Jacobi, C. R. Acad. Sci. Paris, 325, Série I, 1997, 167-170. | MR | Zbl
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