Convex Optimization without Projection Steps

@article{Jaggi2011ConvexOW,
  title={Convex Optimization without Projection Steps},
  author={Martin Jaggi},
  journal={CoRR},
  year={2011},
  volume={abs/1108.1170}
}
We study the general problem of minimizing a convex function over a compact convex domain. We will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe [FW56], that does not need projection steps in order to stay inside the optimization domain. Instead of a projection step, the linearized problem defined by a current subgradient is solved, which gives a step direction that will naturally stay in the domain. Our framework generalizes the sparse greedy… CONTINUE READING
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