Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms

@article{Sundaramoorthi2018AcceleratedOI,
  title={Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms},
  author={Ganesh Sundaramoorthi and Anthony Joseph Yezzi},
  journal={ArXiv},
  year={2018},
  volume={abs/1804.02307}
}
We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by generalizing Nesterov accelerated optimization to the manifold of diffeomorphisms. While our framework is general for infinite dimensional manifolds, we specifically treat the case of diffeomorphisms, motivated by optical flow problems in computer vision… CONTINUE READING
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References

Publications referenced by this paper.
SHOWING 1-10 OF 50 REFERENCES

A Variational Perspective on Accelerated Methods in Optimization

  • Proceedings of the National Academy of Sciences of the United States of America
  • 2016
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

A method of solving a convex programming problem with convergence rate o (1/k2)

——
  • Soviet Mathematics Doklady, vol. 27, 1983, pp. 372–376.
  • 1983
VIEW 16 EXCERPTS
HIGHLY INFLUENTIAL

Determining Optical Flow

VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

Arnol’d, Mathematical methods of classical mechanics

V I.
  • Springer Science & Business Media,
  • 2013
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Geodesic Shooting for Computational Anatomy

  • Journal of Mathematical Imaging and Vision
  • 2005
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL