Characterizations of r-Convex Functions

Y. X. Zhao (), S. Y. Wang () and L. Coladas Uria ()
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Y. X. Zhao: Chinese Academy of Sciences
S. Y. Wang: Chinese Academy of Sciences
L. Coladas Uria: Santiago de Compostela University

Journal of Optimization Theory and Applications, 2010, vol. 145, issue 1, No 11, 186-195

Abstract: 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.

Keywords: Strict r-convexity; r-convexity; Positive-semidefinite matrices; Positive-definite matrices; Convex functions; Quasiconvex functions (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-009-9617-1

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