Three kinds of generalized convexity. (English) Zbl 0838.90117

Summary: This paper gives some properties of quasiconvex, strictly quasiconvex, and strongly quasiconvex functions. Relationships between them are discussed.


90C30 Nonlinear programming
26B25 Convexity of real functions of several variables, generalizations
Full Text: DOI


[1] Arrow, K. I., andEnthoven, A. C.,Quasi-Concave Programming, Econometrica, Vol. 29, pp. 779–800, 1961. · Zbl 0104.14302
[2] Avriel, M.,Nonlinear Programming: Analysis and Methods, Prentice Hall, Englewood Cliffs, New Jersey, 1976. · Zbl 0361.90035
[3] Bazaraa, M. S., andShetty, C. M.,Nonlinear Programming: Theory and Algorithms, John Wiley and Sons, New York, New York, 1979. · Zbl 0476.90035
[4] Greenberg, H. J., andPierskalla, W. P.,A Review of Quasiconvex Functions, Operations Research, Vol. 19, pp. 1553–1570, 1971. · Zbl 0228.26012
[5] Jeyakumar, V., andGwinner, J.,Inequality Systems and Optimization, Journal of Mathematical Analysis and Applications, Vol. 159, pp. 51–71, 1991. · Zbl 0734.90089
[6] Avriel, M., Diewert, W. E., Schaible, S., andZang, I.,Generalized Concavity, Plenum Publishing Corporation, New York, New York, 1988.
[7] Roberts, A. W., andVarberg, D. E.,Convex Functions, Academic Press, New York, New York, 1973. · Zbl 0271.26009
[8] Ponstein, J.,Seven Kinds of Convexity, SIAM Review, Vol. 9, pp. 115–119, 1967. · Zbl 0164.06501
[9] Karamardian, S.,Strictly Quasiconvex (Concave) Functions and Duality in Mathematical Programming, Journal of Mathematical Analysis and Applications, Vol. 20, pp 344–358, 1967. · Zbl 0157.49603
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.