Characterizations of <Emphasis Type="Italic">r</Emphasis>-Convex Functions |
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Authors: | Y X Zhao S Y Wang L Coladas Uria |
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Institution: | (3) Dept. Computer Sci. and Operations Research, North Dakota State Univ., 258 IACC Building, Fargo, ND 58105, USA |
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Abstract: | This paper discusses some properties of r-convexity and its relations with some other types of convexity. A characterization of convex functions in terms of r-convexity is given without assuming differentiability. The concept of strict r-convexity is introduced. For a twice continuously differentiable function f, it is shown that the strict r-convexity of f is equivalent to a certain condition on ∇
2
f. Further, it is shown that this condition is satisfied by quasiconvex functions satisfying a less stringent condition. |
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