Multivariate convex approximation and least-norm convex data-smoothing

Authors:
Alex Y. D. Siem;Dick den Hertog;Aswin L. Hoffmann
Affiliations:
Department of Econometrics and Operations Research/Center for Economic Research (CentER), Tilburg University, Tilburg, LE, The Netherlands;Department of Econometrics and Operations Research/Center for Economic Research (CentER), Tilburg University, Tilburg, LE, The Netherlands;Department of Radiation Oncology, Radboud University Nijmegen Medical Centre, Nijmegen, GA, The Netherlands
Venue:
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
Year:
2006

Citing 2
Cited 1

The convergence rate of the sandwich algorithm for approximating convex functions

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Convex Optimization

Convex Optimization

A Method for Approximating Univariate Convex Functions Using Only Function Value Evaluations

INFORMS Journal on Computing

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Abstract

The main contents of this paper is two-fold. First, we present a method to approximate multivariate convex functions by piecewise linear upper and lower bounds. We consider a method that is based on function evaluations only. However, to use this method, the data have to be convex. Unfortunately, even if the underlying function is convex, this is not always the case due to (numerical) errors. Therefore, secondly, we present a multivariate data-smoothing method that smooths nonconvex data. We consider both the case that we have only function evaluations and the case that we also have derivative information. Furthermore, we show that our methods are polynomial time methods. We illustrate this methodology by applying it to some examples.