# Geometric Optimization Methods for Adaptive Filtering

arXiv: https://arxiv.org/abs/1305.1886 · HTML: https://mlsanity.com/paper/1305.1886/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2013.

## Built on by (most cited first, 4 of 4)

- [Tensor completion using geodesics on Segre manifolds](https://mlsanity.com/paper/2108.00735/) (2021)
- [Unsupervised Learning Discriminative MIG Detectors in Nonhomogeneous Clutter](https://mlsanity.com/paper/2204.11278/) (2022)
- [Parallel transport on matrix manifolds and Exponential Action](https://mlsanity.com/paper/2408.06054/) (2024)
- [Accelerated Optimization Landscape of Linear-Quadratic Regulator](https://mlsanity.com/paper/2307.03590/) (2023)

## Abstract (arXiv)

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and adaptive control. A new point of view is offered for the constrained optimization problem. Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds. Several algorithms are presented and their convergence properties are analyzed employing the Riemannian structure of the manifold. Specifically, two new algorithms, which can be thought of as Newton's method and the conjugate gradient method on Riemannian manifolds, are presented and shown to possess quadratic and superlinear convergence, respectively. These methods are applied to several eigenvalue and singular value problems, which are posed as constrained optimization problems. ...