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-representation of subdifferentials of directionally Lipschitz functions
Authors:
Alejandro Jofré and Lionel Thibault
Journal:
Proc. Amer. Math. Soc. 110 (1990), 117-123
MSC:
Primary 90C48; Secondary 46G05, 49A52, 58C20, 90C25
MathSciNet review:
1015680
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Abstract: Subdifferentials of convex functions and some regular functions are expressed in terms of limiting gradients at points in a given dense subset of .
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- [1]
- J. Borwein and H. M. Strojwas, Proximal analysis and boundaries of closed set in space II: applications (to appear).
- [2]
- S. Chu-Chung, Remarques sur le gradient généralisé, J. Math. Pures Appl. 61 (1982), 301-310. MR 690398 (84d:58008)
- [3]
- F. H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247-262. MR 0367131 (51:3373)
- [4]
- -, Nonsmooth analysis and optimization, Wiley-Interscience, New York, 1983.
- [5]
- R. Correa and A. Jofre, Tangentially continuous directional derivatives in nonsmooth analysis, J. Optim. Theory Appl. (to appear). MR 993912 (90h:49009)
- [6]
- R. Correa and L. Thibault, Subdifferential analysis of bivariate separately regular functions, J. Math. Anal. Appl. (to appear). MR 1052052 (91b:49018)
- [7]
- J. R. Giles, Convex analysis with application in the differentiation of convex functions, Pitman, 1982. MR 650456 (83g:46001)
- [8]
- J. B. Hiriart-Urruty, A note on the mean value theorem for convex functions, Boll. Un. Mat. Ital. B 17 (1980), 765-775. MR 580556 (82b:26007)
- [9]
- R. Mifflin, Semismooth and semiconvex functions in constrained optimization, SIAM J. Control. Optim. 15 (1977), 959-972. MR 0461556 (57:1541)
- [10]
- R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, NJ, 1970.
- [11]
- -, Generalized directional derivatives and subgradients of nonconvex functions, Canad. J. Math. 32 (1980), 257-280. MR 571922 (81f:49006)
- [12]
- -, Directionally Lipschitzian functions and subdifferential calculus, Proc. London Math. Soc. 39 (1979), 331-355. MR 548983 (80j:46070)
- [13]
- -, Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization, Math. Oper. Res. 6 (1981), 424-436. MR 629642 (83m:90088)
- [14]
- L. Thibault, On generalized differentials and subdifferentials of Lipschitz vector-valued functions, Nonlinear. Anal. 6 (1982), 1037-1053. MR 678055 (85e:58020)
- [15]
- J. S. Treiman, Clarke's gradients and epsilon-subgradients in Banach spaces, Trans. Amer. Math. Soc. 294 (1986), 65-78. MR 819935 (87d:90188)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-1015680-3
PII:
S 0002-9939(1990)1015680-3
Keywords:
Directionally Lipschitz functions,
pseudoregular functions,
weak Asplund spaces
Article copyright:
© Copyright 1990 American Mathematical Society
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