The Effect of Transformations on the Approximation of Univariate (Convex) Functions with Applications to Pareto Curves

A.Y.D. Siem, D. den Hertog, A.L. Hoffmann

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Abstract

In the literature, methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed.We study the effect of the use of increasing convex or increasing concave transformations on the approximation of univariate (convex) functions.In this paper, we show that these transformations can be used to construct upper and lower bounds for nonconvex functions.Moreover, we show that by using such transformations of the input variable or the output variable, we obtain tighter upper and lower bounds for the approximation of convex functions than without these approximations.We show that these transformations can be applied to the approximation of a (convex) Pareto curve that is associated with a (convex) bi-objective optimization problem.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages23
Volume2006-66
Publication statusPublished - 2006

Publication series

NameCentER Discussion Paper
Volume2006-66

Keywords

  • approximation theory
  • convexity
  • convex/concave transformation
  • Pareto curve

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