A Complete Derivation of Complex Circle Manifold (CCM) Riemannian manifold Optimization Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908483873406976 |
|---|---|
| author | Tabrizi, Amirreza Mirmohammadi, Mohammad Hadi |
| author_facet | Tabrizi, Amirreza Mirmohammadi, Mohammad Hadi |
| contents | After reviewing manifold optimization techniques in applications like MIMO communication systems, phased array beamforming, radar, and control theory, we observed that the Complex Circle Manifold (CCM) is widely employed, yet its foundational relations and equations lack a rigorous, self-contained derivation in the literature. This paper provides a systematic and rigorous proof of CCM's key properties, including its tangent space and Riemannian gradient operations, with explicit connections to real-world optimization problems. Our work aims to serve as a unified reference for researchers and practitioners applying CCM Manifold Optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07396 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Complete Derivation of Complex Circle Manifold (CCM) Riemannian manifold Optimization Equations Tabrizi, Amirreza Mirmohammadi, Mohammad Hadi Optimization and Control Complex Variables Differential Geometry After reviewing manifold optimization techniques in applications like MIMO communication systems, phased array beamforming, radar, and control theory, we observed that the Complex Circle Manifold (CCM) is widely employed, yet its foundational relations and equations lack a rigorous, self-contained derivation in the literature. This paper provides a systematic and rigorous proof of CCM's key properties, including its tangent space and Riemannian gradient operations, with explicit connections to real-world optimization problems. Our work aims to serve as a unified reference for researchers and practitioners applying CCM Manifold Optimization. |
| title | A Complete Derivation of Complex Circle Manifold (CCM) Riemannian manifold Optimization Equations |
| topic | Optimization and Control Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2508.07396 |