Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm

  title={Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm},
  author={Kenneth L. Clarkson},
  journal={ACM Trans. Algorithms},
  • K. Clarkson
  • Published 20 January 2008
  • Computer Science
  • ACM Trans. Algorithms
The problem of maximizing a concave function <i>f</i>(<i>x</i>) in a simplex <i>S</i> can be solved approximately by a simple greedy algorithm. For given <i>k</i>, the algorithm can find a point <i>x</i>(<i>k</i>) on a <i>k</i>-dimensional face of <i>S</i>, such that <i>f</i>(<i>x</i>(<i>k</i>)) ≥ <i>f</i>(<i>x</i>*) - <i>O</i>(1/<i>k</i>). Here <i>f</i>(<i>x</i>*) is the maximum value of <i>f</i> in <i>S.</i> This algorithm and analysis were known before, and related to problems of statistics… 

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