论文信息 - On the convexifiability of pseudoconvex C2-functions

On the convexifiability of pseudoconvex C2-functions

We present new criteria that characterize functions which are convex transformable by a suitable strictly increasing function. We concentrate on twice continuously differentiable pseudoconvex and strictly pseudoconvex functions, and derive conditions which are both necessary and sufficient for these functions to be convex transformable.

Siegfried Schaible | Israel Zang | S. Schaible | I. Zang

[1] W. Fenchel. Convex cones, sets, and functions , 1953 .

[2] Mordecai Avriel,et al. r-convex functions , 1972, Math. Program..

[3] Siegfried Schaible,et al. Second order characterizations of pseudoconvex functions , 1975, Math. Program..

[4] Israel Zang,et al. Nine kinds of quasiconcavity and concavity , 1981 .

[5] Siegfried Schaible,et al. Second-order characterizations of pseudoconvex quadratic functions , 1977 .

[6] On a close relation between quasi-convex and convex functions and related investigations , 1973 .

[7] D. H. Jacobson. A GENERALIZATION OF FINSLER'S THEOREM FOR QUADRATIC INEQUALITIES AND EQUALITIES , 1976 .

[8] Paul Pinsler. Über das Vorkommen definiter und semidefiniter Formen in Scharen quadratischer Formen , 1936 .

[9] Jean-Pierre Crouzeix. Conditions for Convexity of Quasiconvex Functions , 1980, Math. Oper. Res..

[10] Siegfried Schaible,et al. Quasiconvex, pseudoconvex, and strictly pseudoconvex quadratic functions , 1981 .

[11] Yakar Kannai,et al. Concavifiability and constructions of concave utility functions , 1977 .

[12] Siegfried Schaible. Quasi-concavity and pseudo-concavity of cubic functions , 1973, Math. Program..