Hidden Convexity, Optimization, and Algorithms on Rotation Matrices
成果类型：
Article
署名作者：
Ramachandran, Akshay; Shu, Kevin; Wang, Alex L.
署名单位：
University System of Georgia; Georgia Institute of Technology; Purdue University System; Purdue University
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2023.0114
发表日期：
2025
关键词：
摘要：
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices SO(n). Such problems are non-convex because of the constraint X E SO(n). Nonetheless, we show that certain linear images of SO(n) are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. Our main technical contributions show that any two-dimensional image of SO(n) is convex and that the projection of SO(n) onto its strict upper triangular entries is convex. These results allow us to construct exact convex reformulations for constrained optimization problems over SO(n) with a single constraint or with constraints defined by low-rank matrices. Both of these results are maximal in a formal sense.
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