Fuzzy Principles and Characterization of Trustworthiness

Set-Valued Analysis

Volumn 6, Issue 3, 1998, Pages 265-276

  Ioffe, Alexander ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Extremal principle; Fuzzy principles; Multidimensional mean value theorem; Subdifferentiability space; Subdifferential; Trustworthy space

Indexed keywords

EID: 0000775811     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008614315547     Document Type: Article

References (19)

1. Aussel, D., Corvellec, J.-N. and Lassonde, M.: Mean value property and subdifferential criteria for lower semicontinuous functions, Trans. Amer. Math. Soc. 347 (1995), 4147-4161.
2. Borwein, J. M. and Ioffe, A. D.: Proximal analysis in smooth spaces, Set-Valued Anal. 4 (1996), 1-24.
3. Borwein, J. M., Treiman, J. and Zhu, Q. J.: Partially smooth variational principles and applications, CECM, Res. Report, 96-088, 1996.
4. Borwein, J. M. and Zhu, Q. J.: Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity, SIAM J. Control Optim. 34 (1996), 1576-1991.
5. Clarke, F. H. and Ledyaev, Yu. S.: Mean value inequalities in Hilbert spaces, Trans. Amer. Math. Soc. 344 (1994), 307-324.
6. Fabian, M.: On classes of subdifferentiability spaces of Ioffe, Nonlinear Anal. 12 (1988), 63-74.
7. Fabian, M.: Subdifferentiability and trustworthiness in the light of the new variational principle of Borwein and Preiss, Acta Univ. Carolinae 30 (1989), 51-56.
8. Ioffe, A. D.: On subdifferentiability spaces, Ann. New York Acad. Sci. 410 (1983), 107-119.
9. Ioffe, A. D.: Calculus of Dini subdifferentials of functions and contingent derivatives of set-valued maps, Nonlinear Anal. 8 (1984), 517-539.
10. Ioffe, A. D.: Approximate subdifferentials and applications 3. The metric theory, Mathematika 36 (1989), 1-38.
11. Ioffe, A. D.: Proximal analysis and approximate subdifferentials, J. London Math. Soc. 41 (1990), 175-192.
12. Ioffe, A. D. and Penot, J.-P.: Subdifferentials of performance functions and calculus of coderivatives of set-valued mappings, Serdica Math. J. 22 (1996), 359-384.
13. Ioffe, A. D. and Rockafellar, R. T.: The Euler and Weierstrass conditions for nonsmooth variational problems, Calc. Var. Partial Differential Equations 4 (1996), 59-87.
14. Kruger, A. Ya. and Mordukhovich, B. Sh.: Extremal points and Euler characterization in nonsmooth optimization, Doklady Akad. Nauk BSSR 24 (1980), 684-687.
15. Lassonde, M.: First order rules in nonsmooth constrained optimization, Preprint, 1998.
16. Mordukhovich, B. Sh. and Shao, Y.: Extremal characterization of Asplund spaces, Proc. Amer. Math. Soc. 124 (1996), 197-205.
17. Rockafellar, R. T. and Wets, R. J. B.: Variational Analysis, Springer-Verlag, New York, 1997.
18. Zhu, Q. J.: The equivalence of several basic theorems for subdifferentials, Set-Valued Anal. 6 (1998), 171-185.
19. Zhu, Q. J.: Clarke-Ledyaev mean value inequality in smooth Banach spaces, CECM Research Report 96-78, 1996, Nonlinear Anal., to appear.