Free Access
Issue |
ESAIM: COCV
Volume 19, Number 3, July-September 2013
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Page(s) | 701 - 709 | |
DOI | https://doi.org/10.1051/cocv/2012029 | |
Published online | 17 May 2013 |
- E. Asplund, Fréchet differentiability of convex functions. Acta Math. 121 (1968) 31–47. [CrossRef] [MathSciNet] [Google Scholar]
- E. Asplund, Čebysev sets in Hilbert spaces. Trans. Amer. Math. Soc. 9 (1969) 235–240. [Google Scholar]
- E. Asplund, Differentiability of the metric projection in finite-dimensional Euclidean spaces. Proc. Amer. Math. Soc. 38 (1973) 218–219. [MathSciNet] [Google Scholar]
- E. Asplund and R.T. Rockafellar, Gradients of convex functions. Trans. Amer. Math. Soc. 139 (1969) 443–467. [CrossRef] [MathSciNet] [Google Scholar]
- H.H. Bauschke, J.M. Borwein and P.L. Combettes, Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces. Commun. Contemp. Math. 3 (2001) 615–647. [CrossRef] [MathSciNet] [Google Scholar]
- J. Blatter, Weiteste Punkte und nächste Punkte. Rev. Roum. Math. Pures Appl. 14 (1969) 615–621. [Google Scholar]
- J. M. Borwein and J. D. Vanderwerff, Convex Functions: Constructions, Characterizations and Counterexamples. Encyclopedia of Mathematics and its Applications, vol. 109. Cambridge University Press, Cambridge (2010). [Google Scholar]
- F.H. Clarke, R.J. Stern and P.R. Wolenski, Proximal smoothness and the lower-C2 property. J. Conv. Anal. 2 (1995) 117–144. [Google Scholar]
- S. Cobzaş, Geometric properties of Banach spaces and the existence of nearest and farthest points. Abstract Appl. Anal. 3 (2005) 259–285. [CrossRef] [Google Scholar]
- A.L. Dontchev and T. Zolezzi, Well-Posed Optimization Problems. Springer-Verlag, Berlin (1993). [Google Scholar]
- N.V. Efimov and S.B. Steckin, Approximative compactness and Čebysev sets. Soviet Math. Dokl. 2 (1961) 1226–1228. [Google Scholar]
- S. Fitzpatrick, Metric projections and the differentiability of distance functions. Bull. Austral. Math. Soc. 22 (1980) 291–312. [CrossRef] [MathSciNet] [Google Scholar]
- J.-B. Hiriart-Urruty, Ensembles de Tchebychev vs. ensembles convexes: l’état de la situation vu via l’analyse convexe non lisse. Ann. Sc. Math. Québec 22 (1998) 47–62. [Google Scholar]
- J.-B. Hiriart-Urruty, La conjecture des points les plus eloignés revisitée. Ann. Sci. Math. Québec 29 (2005) 197–214. [Google Scholar]
- V. Klee, Convexity of Chebyshev sets. Math. Ann. 142 (1961) 292–304 [CrossRef] [MathSciNet] [Google Scholar]
- M. Lassonde, Asplund spaces, Stegall variational principle and the RNP. Set-Valued Var. Anal. 17 (2009) 183–193. [CrossRef] [MathSciNet] [Google Scholar]
- J.-J. Moreau, Fonctionnelles Convexes, Collège de France, 1966. Republished by the “Tor Vergata” University, Rome (2003). [Google Scholar]
- T.D. Narang, A study of farthest points. Nieuw Arch. Voor Wiscunde 3 (1977) XXV 54–79. [Google Scholar]
- B.B. Panda and O.P. Kapoor, On farthest points of sets. J. Math. Anal. Appl. 62 (1978) 345–353. [CrossRef] [Google Scholar]
- R.R. Phelps, Convex Functions, Monotone Operators and Differentiability. Lect. Notes Math., vol. 1364. Springer-Verlag (1989). [Google Scholar]
- T. Precupanu, Relationships between farthest point problem and best approximation problem. Anal. Sci. Univ. AI. I. Cuza, Mat. 57 (2011) 1–12. [Google Scholar]
- V. Soloviov, Duality for nonconvex optimization and its applications. Anal. Math. 19 (1993) 297–315. [CrossRef] [MathSciNet] [Google Scholar]
- V. Soloviov, Characterization of convexity in terms of smoothness. Unpublished report, Moscow Aviation Institute (1995). [Google Scholar]
- T. Stromberg, Duality between Fréchet differentiability and strong convexity. Positivity 15 (2011) 527–536. [CrossRef] [MathSciNet] [Google Scholar]
- M. Volle and J.-B. Hiriart-Urruty, A characterization of essentially strictly convex functions in reflexive Banach spaces. Nonlinear Anal. 75 (2012) 1617–1622. [CrossRef] [MathSciNet] [Google Scholar]
- M. Volle and C. Zălinescu, On strongly adequate functions on Banach spaces. J. Convex Anal. (to appear). [Google Scholar]
- X. Wang, On Chebyshev functions and Klee functions. J. Math. Anal. Appl. 368 (2010) 293–310. [CrossRef] [Google Scholar]
- C. Zălinescu, Convex Analysis in General Vector Spaces. World Scientific, River Edge, N.J. (2002). [Google Scholar]
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