On relations among the generalized second-order directional derivatives

 Access to full text

 Full (PDF)

1. [1] J.M. Borwein, M. Fabián, On generic second-order Gâteaux differentiability, Nonlinear Anal. T.M.A 20 (1993), 1373-1382. Zbl0843.46027
2. [2] J.M. Borwein and D. Noll, Second-order differentiability of convex functions in Banach spaces, Trans. Amer. Math. Soc. 342 (1994), 43-81. Zbl0802.46027
3. [3] A. Ben-Tal and J. Zowe, Directional derivatives in nonsmooth optimization, J. Optim. Theory Appl. 47 (1985), 483-490. Zbl0556.90074
4. [4] F.H. Clarke, Necessary conditions for nonsmooth problems in optimal control and the calculus of variations, Ph.D. thesis, Univ. of Washington 1973. 
5. [5] F.H. Clarke, Optimization and nonsmooth analysis, J. Wiley, New York 1983. Zbl0582.49001
6. [6] R. Cominetti, Equivalence between the classes of $C^{1,1}$ and twice locally Lipschitzian functions, Ph.D. thesis, Université Blaise Pascal 1989. 
7. [7] R. Cominetti and R. Correa, A generalized second-order derivative in nonsmooth optimization, SIAM J. Control Optim. 28 (1990), 789-809. Zbl0714.49020
8. [8] W.L. Chan, L.R. Huang and K.F. Ng, On generalized second-order derivatives and Taylor expansions in nosmooth optimiyation, SIAM J. Control Optim. 32 (1994), 789-809. 
9. [9] P.G. Georgiev and N.P. Zlateva, Second-order subdifferentials of $C^{1,1}$ functions and optimality conditions, Set-Valued Analysis 4 (1996), 101-117. Zbl0864.49012
10. [10] J.B. Hiriart-Urruty and C. Lemarchal, Convex Analysis nad Minimization Algorithms, Springer Verlag, Berlin 1993. 
11. [11] L.R. Huang and K.F. Ng, On some relations between Chaney's generalized second-order directional derivative and that of Ben-Tal and Zowe, SIAM J. Control Optim. 34 (1996), 1220-1234. Zbl0877.49019
12. [12] V. Jeyakumar and X.Q. Yang, Approximate generalized Hessians and Taylor's expansions for continously Gâteaux differentiable functions, Nonlinear Anal. T.M.A 36 (1999), 353-368. Zbl0931.49011
13. [13] G. Lebourg, Generic differentiability of Lipschitz functions, Trans. Amer. Math. Soc. 256 (1979), 125-144. Zbl0435.46031
14. [14] Y. Maruyama, Second-order necessary conditions for nonlinear problems in Banach spases and their applications to optimal control problems, Math. Programming 41 (1988), 73-96. 
15. [15] P. Michel and J.P. Penot, Second-order moderate derivatives, Nonlinear Anal. T.M.A 22 (1994), 809-821. Zbl0810.49017
16. [16] K. Pastor, Generalized second-order directional derivatives for locally Lipschitz functions, Preprint no. 17/2001 of Palacký Univerzity, Olomouc. 
17. [17] R.T. Rockafellar, Characterization of the subdifferentials of convex functions, Pacific J. Math. 17 (1966), 497-509. Zbl0145.15901
18. [18] R.T. Rockafellar, Second-order optimality conditions in nonlinear programming obtained by way of epi-derivatives, Math. Oper. Res. 14 (1989), 462-484. Zbl0698.90070
19. [19] X.Q. Yang, On relations and applications of generalized second-order directional derivatives, Non. Anal. T.M.A 36 (1999), 595-614. Zbl0990.49016
20. [20] X.Q. Yang, On second-order directional derivatives, Non. Anal. T.M.A 26, 55-66. Zbl0839.90138