Abstract
The following question arises in stochastic programming: how can one approximate a noisy convex function with a convex quadratic function that is optimal in some sense. Using several approaches for constructing convex approximations we present some optimization models yielding convex quadratic regressions that are optimal approximations in L 1, L ∞ and L 2 norm. Extensive numerical experiments to investigate the behavior of the proposed methods are also performed.
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Deák, I., Pólik, I., Prékopa, A. et al. Convex approximations in stochastic programming by semidefinite programming. Ann Oper Res 200, 171–182 (2012). https://doi.org/10.1007/s10479-011-0986-0
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DOI: https://doi.org/10.1007/s10479-011-0986-0