A Simple Way to Prove the Characterization of Differentiable Quasiconvex Functions

DOI: 10.4236/am.2014.58114   PDF   HTML     4,237 Downloads   5,185 Views   Citations


We give a short and easy proof of the characterization of differentiable quasiconvex functions.

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Giorgi, G. (2014) A Simple Way to Prove the Characterization of Differentiable Quasiconvex Functions. Applied Mathematics, 5, 1226-1228. doi: 10.4236/am.2014.58114.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] De Finetti, B. (1949) Sulle Stratificazioni Convesse. Annali di Matematica Pura ed Applicata, 30, 173-183.
[2] Fenchel, W. (1953) Convex Cones, Sets and Functions. Lecture Notes, Princeton University, Princeton.
[3] Arrow, K.J. and Enthoven, A.C. (1961) Quasi-Concave Programming. Econometrica, 29, 779-800.
[4] Avriel, M. (1976) Nonlinear Programming: Analysis and Methods. Prentice-Hall, Englewood Cliffs.
[5] Avriel, M., Diewert, W.E., Schaible, S. and Zang, I. (1988) Generalized Concavity. Plenum Press, New York.
[6] Bazaraa, M.S. and Shetty, C.M. (1976) Foundations of Optimization. Springer Verlag, Berlin.
[7] Bazaraa, M.S., Sherali, H.D. and Shetty, C.M. (1993) Nonlinear Programming. John Wiley & Sons, New York.
[8] Kemp, M.C. and Kimura, Y. (1978) Introduction to Mathematical Economics. Springer Verlag, New York.
[9] Mangasarian, O.L. (1969) Nonlinear Programming. McGraw-Hill, New York.
[10] Ponstein, J. (1967) Seven Kinds of Convexity. SIAM Review, 9, 115-119.
[11] Simon, C.P. and Blume, L. (1994) Mathematics for Economists. W. W. Norton & Co., New York.
[12] Cambini, A. and Martein, L. (2009) Generalized Convexity and Optimization. Springer, Berlin.
[13] 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.

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