Unconstrained Convex Minimization in Relative Scale

@article{Nesterov2009UnconstrainedCM,
  title={Unconstrained Convex Minimization in Relative Scale},
  author={Yurii Nesterov},
  journal={Math. Oper. Res.},
  year={2009},
  volume={34},
  pages={180-193}
}
In this paper we present a new approach to constructing schemes for unconstrained convex minimization, which compute approximate solutions with a certain relative accuracy. This approach is based on a special conic model of the unconstrained minimization problem. Using a structural model of the objective function we can employ the efficient smoothing technique. The fastest of our algorithms solves a linear programming problem with relative accuracy δ in at most e ·√m (2 + lnm) · ( 1 + 1… CONTINUE READING

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