@article{AIHPC_1989__S6__449_0, author = {Rockafellar, R. T.}, title = {Proto-differentiability of set-valued mappings and its applications in optimization}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {449--482}, publisher = {Gauthier-Villars}, volume = {S6}, year = {1989}, mrnumber = {1019126}, zbl = {0674.90082}, language = {en}, url = {http://www.numdam.org/item/AIHPC_1989__S6__449_0/} }
TY - JOUR AU - Rockafellar, R. T. TI - Proto-differentiability of set-valued mappings and its applications in optimization JO - Annales de l'I.H.P. Analyse non linéaire PY - 1989 SP - 449 EP - 482 VL - S6 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_1989__S6__449_0/ LA - en ID - AIHPC_1989__S6__449_0 ER -
%0 Journal Article %A Rockafellar, R. T. %T Proto-differentiability of set-valued mappings and its applications in optimization %J Annales de l'I.H.P. Analyse non linéaire %D 1989 %P 449-482 %V S6 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPC_1989__S6__449_0/ %G en %F AIHPC_1989__S6__449_0
Rockafellar, R. T. Proto-differentiability of set-valued mappings and its applications in optimization. Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989), pp. 449-482. http://www.numdam.org/item/AIHPC_1989__S6__449_0/
1. Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions", Mathematical Analysis and Applications, Part A; Advances in Math. Supplementary Studies, Vol. 7A (Academic Press. 1981), 159-229. | MR | Zbl
, -2. Lipschitz behavior of solutions to convex minimization problems", Math. of Op. Research 9(1984), 87-111. | MR | Zbl
, "3. Applied Nonlinear Analysis, Wiley-Interscience, 1984. | MR | Zbl
and ,4. Differential Inclusions, Springer-Verlag, 1984. | MR | Zbl
and ,5. Inclusions adjointes associées aux trajectoires minimales d'inclusions différentielles", C.R. Acad. Sc. Paris 297(1983), 461-464. | MR | Zbl
, "6. Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions" , Ann. Inst. H. Poincaré: Analyse Non Linéaire 2(1985), 75-99. | Numdam | MR | Zbl
, "7. Local controllability and infinitesimal generators of semigroups of set-valued maps", SIAM J. Control Opt. 25(1987). 412-432. | MR | Zbl
, "8. Generalized gradients and applications", Trans. Amer. Math. Soc. 205(1975), 247-262. | MR | Zbl
. "9. Nonsmooth Analysis and Optimization, Wiley-Interscience, 1983. | MR | Zbl
,10. First and second-order epi-differentiability in nonlinear programming", Trans. Amer. Math. Soc., to appear. | MR | Zbl
, "11. Maximal monotone relations and the second derivatives of nons-mooth functions", Ann. Inst. H. Poincaré: Analyse Non Linéaire 2(1985), 167-184. | Numdam | MR | Zbl
, "12. "Generalized second derivatives of convex functions and saddle functions", forthcoming. | MR | Zbl
, -13. Introduction à la Géométrie Infuitesimale Directe, Gauthier-Villars, Paris. 1932. | JFM | Zbl
,14. Second-order sensitivity anlysis and asymptotic theory of parameterized nonlinear programs", Math. Prog. 33(1985), 280-299. | MR | Zbl
, -15. Convex Analysis, Princeton Univ. Press, 1970. | MR | Zbl
,16. Lipschitzian properties of multifunctions", Nonlin. Anal. Th. Math. Appl. 9(1985), 867-885. | MR | Zbl
, -17. Generalized equations and their solution, part I: basic theory". Math. Programming Study 10(1979). 128-141. | MR | Zbl
, "18. Generalized equations and their solutions, part II: applications to nonlinear programming", Math. Programming Study 19(1982), 200-221. | MR | Zbl
, "19. Some continuity properties of polyhedral multifunctions", Math. Programming Study 14(1981), 206-214. | MR | Zbl
, "20. Tangent sets' calculus and necessary conditions for extremality", SIAM J. Control Opt. 20(1982), 563-574. | MR | Zbl
, "