A Unified Dynamical Framework for Optimization on Grassmann Manifolds via Dual Semidefinite Programming
Fuente:
Zenodo
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Recurso digital |
| Pubblicazione: |
Zenodo
2026
|
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866901849782616064 |
|---|---|
| author | Zhang, Jincheng |
| author_facet | Zhang, Jincheng |
| contents | <p><span>This paper proposes a novel optimization framework that combines the structured convex optimization advantages of Dual Semidefinite Programming (Dual SDP) with geometric constraints on Grassmann manifolds, forming a "Dual Grassmann Manifold Dynamic Optimization Equation." This method achieves continuous dynamic evolution of constrained semidefinite optimization problems by introducing dual variables and Lagrange multipliers onto the manifold, while preserving global convergence guarantees. Theoretical analysis shows that the constructed equation guarantees exponential convergence under convex constraints and effectively handles nonlinear manifold constraints. Numerical experiments verify the superior performance of this method in problems such as low-rank matrix recovery, signal processing, and quantum state optimization. The proposed method has potential theoretical generalization value, providing a unified theoretical tool for structured semidefinite optimization and manifold optimization.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19277078 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Unified Dynamical Framework for Optimization on Grassmann Manifolds via Dual Semidefinite Programming Zhang, Jincheng <p><span>This paper proposes a novel optimization framework that combines the structured convex optimization advantages of Dual Semidefinite Programming (Dual SDP) with geometric constraints on Grassmann manifolds, forming a "Dual Grassmann Manifold Dynamic Optimization Equation." This method achieves continuous dynamic evolution of constrained semidefinite optimization problems by introducing dual variables and Lagrange multipliers onto the manifold, while preserving global convergence guarantees. Theoretical analysis shows that the constructed equation guarantees exponential convergence under convex constraints and effectively handles nonlinear manifold constraints. Numerical experiments verify the superior performance of this method in problems such as low-rank matrix recovery, signal processing, and quantum state optimization. The proposed method has potential theoretical generalization value, providing a unified theoretical tool for structured semidefinite optimization and manifold optimization.</span></p> |
| title | A Unified Dynamical Framework for Optimization on Grassmann Manifolds via Dual Semidefinite Programming |
| url | https://doi.org/10.5281/zenodo.19277078 |