Proto-differentiability of set-valued mappings and its applications in optimization

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1. 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. Zbl0484.47034MR634239
2. 2. J.P. Aubin, "Lipschitz behavior of solutions to convex minimization problems", Math. of Op. Research9(1984), 87-111. Zbl0539.90085MR736641
3. 3. J.P. Aubin and I., Ekeland, Applied Nonlinear Analysis, Wiley-Interscience, 1984. Zbl0641.47066MR749753
4. 4. J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, 1984. Zbl0538.34007MR755330
5. 5. H. Frankowska, "Inclusions adjointes associées aux trajectoires minimales d'inclusions différentielles", C.R. Acad. Sc. Paris297(1983), 461-464. Zbl0532.49024MR736244
6. 6. H. Frankowska, "Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions" , Ann. Inst. H. Poincaré: Analyse Non Linéaire2(1985), 75-99. Zbl0576.49013MR794001
7. 7. H. Frankowska, "Local controllability and infinitesimal generators of semigroups of set-valued maps", SIAM J. Control Opt.25(1987). 412-432. Zbl0625.49015MR877070
8. 8. F.H. Clarke. "Generalized gradients and applications", Trans. Amer. Math. Soc.205(1975), 247-262. Zbl0307.26012MR367131
9. 9. F.H. Clarke, Nonsmooth Analysis and Optimization, Wiley-Interscience, 1983. Zbl0582.49001MR709590
10. 10. R.T. Rockafellar, "First and second-order epi-differentiability in nonlinear programming", Trans. Amer. Math. Soc., to appear. Zbl0655.49010MR936806
11. 11. R.T. Rockafellar, "Maximal monotone relations and the second derivatives of nons-mooth functions", Ann. Inst. H. Poincaré: Analyse Non Linéaire2(1985), 167-184. Zbl0581.49009MR797269
12. 12. R.T. Rockafellar, -"Generalized second derivatives of convex functions and saddle functions", forthcoming. Zbl0712.49011MR1031242
13. 13. G. Bouligand, Introduction à la Géométrie Infuitesimale Directe, Gauthier-Villars, Paris. 1932. Zbl0005.37501JFM58.0086.03
14. 14. A. Shapiro, -Second-order sensitivity anlysis and asymptotic theory of parameterized nonlinear programs", Math. Prog.33(1985), 280-299. Zbl0579.90088MR816106
15. 15. R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, 1970. Zbl0193.18401MR274683
16. 16. R.T. Rockafellar, -Lipschitzian properties of multifunctions", Nonlin. Anal. Th. Math. Appl.9(1985), 867-885. Zbl0573.54011MR799890
17. 17. S.M. Robinson, "Generalized equations and their solution, part I: basic theory". Math. Programming Study10(1979). 128-141. Zbl0404.90093MR527064
18. 18. S.M. Robinson, "Generalized equations and their solutions, part II: applications to nonlinear programming", Math. Programming Study19(1982), 200-221. Zbl0495.90077MR669732
19. 19. S.M. Robinson, "Some continuity properties of polyhedral multifunctions", Math. Programming Study14(1981), 206-214. Zbl0449.90090MR600130
20. 20. C. Ursescu, "Tangent sets' calculus and necessary conditions for extremality", SIAM J. Control Opt.20(1982), 563-574. Zbl0488.49009MR661033

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