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A. Y. D. Siem, D. den Hertog and A. L. Hoffmann, “A Method for Approximating Univariate Convex Functions Using Only Function Value Evaluations,” Center Discussion Paper, Vol. 67, 2007, pp. 1-26.

has been cited by the following article:

• TITLE: Some Remarks on Application of Sandwich Methods in the Minimum Cost Flow Problem

  AUTHORS: Marta Kostrzewska, Leslaw Socha

  KEYWORDS: Bicriteria Network Cost Flow Problem; Sandwich Algorithms; Efficient Frontier; Stochastic Costs

  JOURNAL NAME: American Journal of Operations Research, Vol.2 No.1, March 14, 2012

  ABSTRACT: In this paper, two new sandwich algorithms for the convex curve approximation are introduced. The proofs of the linear convergence property of the first method and the quadratic convergence property of the second method are given. The methods are applied to approximate the efficient frontier of the stochastic minimum cost flow problem with the moment bicriterion. Two numerical examples including the comparison of the proposed algorithms with two other literature derivative free methods are given.