Abstract
We derive worst-case bounds, with respect to the L p norm, on the error achieved by algorithms aimed at approximating a concave function of a single variable, through the evaluation of the function and its subgradient at a fixed number of points to be determined. We prove that, for p larger than 1, adaptive algorithms outperform passive ones. Next, for the uniform norm, we propose an improvement of the Sandwich algorithm, based on a dynamic programming formulation of the problem.
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Communicated by Jean-Pierre Crouzeix
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Guérin, J., Marcotte, P. & Savard, G. Approximation in p-Norm of Univariate Concave Functions. J Optim Theory Appl 161, 490–505 (2014). https://doi.org/10.1007/s10957-013-0410-9
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DOI: https://doi.org/10.1007/s10957-013-0410-9