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Two gradient properties of explicitly convex functions

Part of: Functions of several variables General convexity

Published online by Cambridge University Press:  09 April 2009

Xinmin Yang
Xinmin Yang
Affiliation:
Department of Mathematics, Chongqing Normal University, Chongqing 630047, China
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Abstract

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In this paper, two gradient properties of explicit convex functions are given.

Keywords

explicitly convex functiondifferentiablemean-value theorem.

MSC classification

Secondary: 26B25: Convexity, generalizations 52A41: Convex functions and convex programs
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 3 , June 1995 , pp. 404 - 410
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Bazaraa, M. S. and Shetty, C. M., Nonlinear programming: Theory and algorithms (Wiley, New York, 1979).Google Scholar
[2]Karamardian, S. and Schaible, S., ‘Seven kinds of monotone maps’, J. Optim. Theory Appl. 66 (1990), 37–46.CrossRefGoogle Scholar
[3]Roberts, A. W. and Varberg, D. E., Convex functions (New York, 1973).Google Scholar
[4]Rockafellar, R. T., Convex analysis (Princeton University Press, Princeton, 1970).CrossRefGoogle Scholar
[5]Xue, S. and Shen, S., ‘Eleven kinds of convexity’, Chinese Journal Oper. Res. 8 (1989), 72–75.Google Scholar