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Corpus ID: 226976065

Simple Iterative Methods for Linear Optimization over Convex Sets

@article{Dadush2020SimpleIM,
title={Simple Iterative Methods for Linear Optimization over Convex Sets},
author={D. Dadush and Christopher Hojny and S. Huiberts and Stefan Weltge},
journal={ArXiv},
year={2020},
volume={abs/2011.08557}
}

We give simple iterative methods for computing approximately optimal primal and dual solutions for the problem of maximizing a linear functional over a convex set $K$ given by a separation oracle. In contrast to prior work, our algorithms directly output primal and dual solutions and avoid a common requirement of binary search on the objective value.
Under the assumption that $K$ contains a ball of radius $r$ and is contained inside the origin centered ball of radius $R$, using $O(\frac{R^4}{r… CONTINUE READING