Rainer E. Burkard, Horst W. Hamacher, and Günter Rote:

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

Naval Research Logistics 38 (1991), 911-924, (Zbl 755.90066, MR #92h:90098).


We develop an algorithm for computing upper and lower aproximations of an explicitly or implicitly given convex function defined on an interval of length T. The algorithm requires no differentiability assumptions; the error decreases quadratically with the number of iterations. To reach an absolute accuracy of E, the number of iterations is bounded by sqrt(9DT/(8E)), where D is the total slope increase of the function. As an application, we discuss separable convex programs.

Note: A more general treatment of the Sandwich algorithm (with different proofs) is given in the paper The convergence rate of the Sandwich algorithm for approximating convex functions by Günter Rote.

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