491. Low-Rank Semidefinite Programming for Symmetric Tensor Decomposition: An Experimental Study
Invited abstract in session WC-11: Interior point methods and applications - Part II, stream Interior point methods and applications.
Wednesday, 14:00-16:00Room: B100/5017
Authors (first author is the speaker)
| 1. | Yassine Koubaa
|
| Mathematics, Université Cote D'Azur |
Abstract
Semidefinite programming (SDP) has long been a cornerstone in global optimization, particularly in polynomial optimization. Yet its application to tensor decomposition—via the matrix completion of moment (Hankel) matrices—remains relatively underexplored. In this work, we propose an SDP-based formulation aimed at recovering full moment matrices from partial observations, leveraging the intrinsic low-rank structure of Hankel matrices. We analyze and compare different low-rank oriented interior-point methods, based on effective preconditioner for low rank Schur complement matrix such as Loraine, and perturbation-based methods such as IPLR- BB, that naturally drives the solution toward a low-rank structure. Preliminary experiments will benchmark these methods against classical SDP solvers to assess computational efficiency and the quality of the low-rank solutions. We will also present experiments, assessing the strengths and weakness of the approach for tackling the challenges of tensor decomposition.
Keywords
- Conic and semidefinite optimization
- Complexity and efficiency of algorithms
Status: accepted
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