Corpus ID: 221802753

Affine-invariant contracting-point methods for Convex Optimization

@article{Doikov2020AffineinvariantCM,
  title={Affine-invariant contracting-point methods for Convex Optimization},
  author={Nikita Doikov and Y. Nesterov},
  journal={arXiv: Optimization and Control},
  year={2020}
}
In this paper, we develop new affine-invariant algorithms for solving composite con- vex minimization problems with bounded domain. We present a general framework of Contracting-Point methods, which solve at each iteration an auxiliary subproblem re- stricting the smooth part of the objective function onto contraction of the initial domain. This framework provides us with a systematic way for developing optimization methods of different order, endowed with the global complexity bounds. We show… Expand
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