Minimizing within Convex Bodies Using a Convex Hull Method

  title={Minimizing within Convex Bodies Using a Convex Hull Method},
  author={Thomas Lachand-Robert and {\'E}douard Oudet},
  journal={SIAM J. Optim.},
We present numerical methods to solve optimization problems on the space of convex functions or among convex bodies. Hence convexity is a constraint on the admissible objects, whereas the functionals are not required to be convex. To deal with this, our method mixes geometrical and numerical algorithms. We give several applications arising from classical problems in geometry and analysis: Alexandrov's problem of finding a convex body of prescribed surface function; Cheeger's problem of a… 

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