Characteristics of Subdifferentials of Functions

Guo Xingming

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1996 > 17(5): 427-432

Guo Xingming. Characteristics of Subdifferentials of Functions[J]. Applied Mathematics and Mechanics, 1996, 17(5): 427-432.

Citation:

Guo Xingming. Characteristics of Subdifferentials of Functions[J]. Applied Mathematics and Mechanics, 1996, 17(5): 427-432.

Citation:

Guo Xingming. Characteristics of Subdifferentials of Functions[J]. Applied Mathematics and Mechanics, 1996, 17(5): 427-432.

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Characteristics of Subdifferentials of Functions

Guo Xingming

Shanghai Univetsity,Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China

Received Date: 1995-06-16
Publish Date: 1996-05-15

Abstract

Abstract

In the presem paper, some important characteristics of Fenchel-, Frechet-,Hademard-, and Gateaux-Subdifferentials are showed up, and properties of functions, especially convexity of functions, are described by subdifferentials.
- subdifferential,
- generalized mean value theorem,
- convexity,
- Lipschitz,
- monotone

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References(13)

References

[1]	R.T.Rockafeller,Convex Analysis,Princeton Univ.Press,Frinceton,NJ.(1970).
[2]	I.Ekeland and R.Temam,Convex Analysis and Variational Problems,North-Holland,Amsterdam (1976).
[3]	F.H.Clarke,Optimisation and Nonsrnooth Analysis,Wiley,New York (1983).
[4]	J.M.Borwein and H.M.Strojwas,Proximal analysis and boundaries of closed sets in banacli space II: Applications,Canad.J.Math.,39 (1978),428-472.
[5]	Chang Kungching,Variational methods for non-differentiable functionals and their applications to partial differential equations,J.Math.Anal.Appl,80 (1981),102-129.
[6]	E.S.Mistakids and P.D.Panagiotopolus,On the approximation of nonmonotone multivalued problems by monotone subproblems,Camput.Methods Appl.Mech.Engrg..114 (1994),55-76.
[7]	R.T.Rockafellar.Generalized directional derivatives and subgradients of nonconvex functions,Canad.J.Math.,(1980).257-280.
[8]	R.A.Poliquin,Subgradient monotonicify and convex functions,Nonlinear Analysis,14(1990),305-317.
[9]	R.Correa,A.Joffre and L.Thibault,Characterization of lower semicontinuous convex functions,Proc.Amer.Math.Soc..116 (1992),67-72.
[10]	R.Correa,A Joffre and L.Thibault.Subdifferential monotonicity as characterization of convex functions,Numer.Fcn:ct.Anal.Optimiz.,15(1994),531-535.
[11]	D.Zagrodny.Approximate mean value theorem for upper subderivates,Nonlinear Analysis,12 (1988),1413-1428.
[12]	J.M .Borwein and D.Preiss,A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions,Trans.Amer.Marh.Soc.,303.2(1987),517-527
[13]	V.F.Demyanov and L.V.Vasiler.Nondifferentiable Optimization.Inc.Publications Division,New Fork(1985).