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A Simple Way to Prove the Characterization of Differentiable Quasiconvex Functions
Faculty of Economics, University of Pavia, Pavia, Italy
- 1 Faculty of Economics, University of Pavia, Pavia, Italy
Applied Mathematics·Volume 05 (2014)·Pages 1226–1228·Published 24 April 2014·DOI10.4236/am.2014.58114
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Abstract
We give a short and easy proof of the characterization of differentiable quasiconvex functions.
Keywordsasiconvex FunctionsGeneralized Convexity
- De Finetti, B. (1949) Sulle Stratificazioni Convesse. Annali di Matematica Pura ed Applicata, 30, 173-183. http://dx.doi.org/10.1007/BF02415006
- Fenchel, W. (1953) Convex Cones, Sets and Functions. Lecture Notes, Princeton University, Princeton.
- Arrow, K.J. and Enthoven, A.C. (1961) Quasi-Concave Programming. Econometrica, 29, 779-800. http://dx.doi.org/10.2307/1911819
- Avriel, M. (1976) Nonlinear Programming: Analysis and Methods. Prentice-Hall, Englewood Cliffs.
- Avriel, M., Diewert, W.E., Schaible, S. and Zang, I. (1988) Generalized Concavity. Plenum Press, New York. http://dx.doi.org/10.1007/978-1-4684-7600-2
- Bazaraa, M.S. and Shetty, C.M. (1976) Foundations of Optimization. Springer Verlag, Berlin. http://dx.doi.org/10.1007/978-3-642-48294-6
- Bazaraa, M.S., Sherali, H.D. and Shetty, C.M. (1993) Nonlinear Programming. John Wiley & Sons, New York.
- Kemp, M.C. and Kimura, Y. (1978) Introduction to Mathematical Economics. Springer Verlag, New York. http://dx.doi.org/10.1007/978-1-4612-6278-7
- Mangasarian, O.L. (1969) Nonlinear Programming. McGraw-Hill, New York.
- Ponstein, J. (1967) Seven Kinds of Convexity. SIAM Review, 9, 115-119. http://dx.doi.org/10.1137/1009007
- Simon, C.P. and Blume, L. (1994) Mathematics for Economists. W. W. Norton & Co., New York.
- Cambini, A. and Martein, L. (2009) Generalized Convexity and Optimization. Springer, Berlin.
- Crouzeix, J.-P. (2005) Criteria for Generalized Convexity and Generalized Monotonicity in the Differentiable Case. In: Hadjisavvas, N., Komlosi, S. and Schaible, S., Eds., Handbook of Generalized Convexity and Generalized Monotonicity, Springer, New York, 89-119. http://dx.doi.org/10.1007/0-387-23393-8_2