Proto-differentiability of set-valued mappings and its applications in optimization
Annales de l'I.H.P. Analyse non linéaire, Volume S6 (1989), p. 449-482
@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},
     publisher = {Gauthier-Villars},
     volume = {S6},
     year = {1989},
     pages = {449-482},
     zbl = {0674.90082},
     mrnumber = {1019126},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume S6 (1989) pp. 449-482. http://www.numdam.org/item/AIHPC_1989__S6__449_0/

1. J.P. Aubin, -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 634239 | Zbl 0484.47034

2. J.P. Aubin, "Lipschitz behavior of solutions to convex minimization problems", Math. of Op. Research 9(1984), 87-111. | MR 736641 | Zbl 0539.90085

3. J.P. Aubin and I., Ekeland, Applied Nonlinear Analysis, Wiley-Interscience, 1984. | MR 749753 | Zbl 0641.47066

4. J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, 1984. | MR 755330 | Zbl 0538.34007

5. H. Frankowska, "Inclusions adjointes associées aux trajectoires minimales d'inclusions différentielles", C.R. Acad. Sc. Paris 297(1983), 461-464. | MR 736244 | Zbl 0532.49024

6. H. Frankowska, "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 794001 | Zbl 0576.49013

7. H. Frankowska, "Local controllability and infinitesimal generators of semigroups of set-valued maps", SIAM J. Control Opt. 25(1987). 412-432. | MR 877070 | Zbl 0625.49015

8. F.H. Clarke. "Generalized gradients and applications", Trans. Amer. Math. Soc. 205(1975), 247-262. | MR 367131 | Zbl 0307.26012

9. F.H. Clarke, Nonsmooth Analysis and Optimization, Wiley-Interscience, 1983. | MR 709590 | Zbl 0582.49001

10. R.T. Rockafellar, "First and second-order epi-differentiability in nonlinear programming", Trans. Amer. Math. Soc., to appear. | MR 936806 | Zbl 0655.49010

11. R.T. Rockafellar, "Maximal monotone relations and the second derivatives of nons-mooth functions", Ann. Inst. H. Poincaré: Analyse Non Linéaire 2(1985), 167-184. | Numdam | MR 797269 | Zbl 0581.49009

12. R.T. Rockafellar, -"Generalized second derivatives of convex functions and saddle functions", forthcoming. | MR 1031242 | Zbl 0712.49011

13. G. Bouligand, Introduction à la Géométrie Infuitesimale Directe, Gauthier-Villars, Paris. 1932. | JFM 58.0086.03 | Zbl 0005.37501

14. A. Shapiro, -Second-order sensitivity anlysis and asymptotic theory of parameterized nonlinear programs", Math. Prog. 33(1985), 280-299. | MR 816106 | Zbl 0579.90088

15. R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, 1970. | MR 274683 | Zbl 0193.18401

16. R.T. Rockafellar, -Lipschitzian properties of multifunctions", Nonlin. Anal. Th. Math. Appl. 9(1985), 867-885. | MR 799890 | Zbl 0573.54011

17. S.M. Robinson, "Generalized equations and their solution, part I: basic theory". Math. Programming Study 10(1979). 128-141. | MR 527064 | Zbl 0404.90093

18. S.M. Robinson, "Generalized equations and their solutions, part II: applications to nonlinear programming", Math. Programming Study 19(1982), 200-221. | MR 669732 | Zbl 0495.90077

19. S.M. Robinson, "Some continuity properties of polyhedral multifunctions", Math. Programming Study 14(1981), 206-214. | MR 600130 | Zbl 0449.90090

20. C. Ursescu, "Tangent sets' calculus and necessary conditions for extremality", SIAM J. Control Opt. 20(1982), 563-574. | MR 661033 | Zbl 0488.49009