On separable product functions

On separable product functions

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Article ID: iaor19911368
Country: Germany
Volume: 21
Start Page Number: 189
End Page Number: 195
Publication Date: May 1990
Journal: Optimization
Authors: ,
Abstract:

In this paper the question is the following: how to choose a domain where the twice continuously differentiable function G(t)=Π−rnât=1âgi(ti), t∈CℝRn (C is an open convex set) is concave to convex? First necessary and sufficient conditions are obtained for the positive and negative semi-definiteness of the Hessian matrix, then a concavity and a convexity domain will be determined.

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