Sandwich approximation of univariate convex functions with an application to separable convex programming

Sandwich approximation of univariate convex functions with an application to separable convex programming

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Article ID: iaor201523999
Volume: 38
Issue: 6
Start Page Number: 911
End Page Number: 924
Publication Date: Dec 1991
Journal: Naval Research Logistics (NRL)
Authors: , ,
Keywords: approximation, separable problem
Abstract:

In this article an algorithm for computing upper and lower approximations of a (implicitly or explicitly) given convex function h defined on an interval of length T is developed. The approximations can be obtained under weak assumptions on h (in particular, no differentiability), and the error decreases quadratically with the number of iterations. To reach an absolute accuracy of the number of iterations is bounded by , where D is the total increase in slope of h. As an application we discuss separable convex programs.

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