The Effect of Transformations on the Approximation of Univariate (Convex) Functions with Applications to Pareto Curves
AbstractIn 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2006-66.
Date of creation: 2006
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approximation theory; convexity; convex/concave transformation; Pareto curve;
Find related papers by JEL classification:
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
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