Lipschitz Analysis of Generalized Phase Retrievable Matrix Frames

Bălan, Radu; Dock, Chris B.

doi:10.1137/21m1435446

Cited by 4 publications

(2 citation statements)

References 26 publications

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“…We remark that we could have concluded this inequality from [8,Theorem 2.7] where it is also stated. It actually holds for any Z 1 for which Y T Z 1 is symmetric and positive semidefinite using the same argument (in particular for Z 1 replaced with the initial Z).…”

Section: Horizontal Space and Unique Factorizationsmentioning

confidence: 60%

“…For positive semidefinite fixed-rank matrices, this has been worked out in detail in [34]. Additional material, including the complex Hermitian case, can be found in [8]. However, in order to arrive at practical formulas that are useful for our path-following algorithm later on, we will not further refer to the concept of a quotient manifold but directly focus on the injectivity of the map φ on a suitable linear subspace, which we describe in the following section.…”

Section: Preliminaries and Key Assumptionsmentioning

confidence: 99%

See 1 more Smart Citation

Time-Varying Semidefinite Programming: Path Following a Burer--Monteiro Factorization

Bellon¹,

Dressler²,

Kungurtsev³

et al. 2022

Preprint

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We present an online algorithm for time-varying semidefinite programs (TV-SDPs), based on the tracking of the solution trajectory of a low-rank matrix factorization, also known as the Burer-Monteiro factorization, in a path-following procedure. There, a predictorcorrector algorithm solves a sequence of linearized systems. This requires the introduction of a horizontal space constraint to ensure the local injectivity of the low-rank factorization. The method produces a sequence of approximate solutions for the original TV-SDP problem, for which we show that they stay close to the optimal solution path if properly initialized. Numerical experiments for a time-varying Max-Cut SDP relaxation demonstrate the computational advantages of the proposed method for tracking TV-SDPs in terms of runtime compared to off-the-shelf interior point methods.

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Section: Horizontal Space and Unique Factorizationsmentioning

confidence: 60%

Section: Preliminaries and Key Assumptionsmentioning

confidence: 99%

Time-Varying Semidefinite Programming: Path Following a Burer--Monteiro Factorization

Bellon¹,

Dressler²,

Kungurtsev³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

Stable phase retrieval in function spaces

Freeman,

Oikhberg,

Pineau

et al. 2023

Math. Ann.

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Group-Invariant Max Filtering

Cahill,

Iverson,

Mixon

et al. 2024

Found Comput Math

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Given a real inner product space V and a group G of linear isometries, we construct a family of G-invariant real-valued functions on V that we call max filters. In the case where $$V={\mathbb {R}}^d$$ V = R d and G is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where $$V=L^2({\mathbb {R}}^d)$$ V = L 2 ( R d ) and G is the group of translation operators, a max filter exhibits stability to diffeomorphic distortion like that of the scattering transform introduced by Mallat. We establish that max filters are well suited for various classification tasks, both in theory and in practice.

show abstract

Lipschitz Analysis of Generalized Phase Retrievable Matrix Frames

Cited by 4 publications

References 26 publications

Time-Varying Semidefinite Programming: Path Following a Burer--Monteiro Factorization

Time-Varying Semidefinite Programming: Path Following a Burer--Monteiro Factorization

Stable phase retrieval in function spaces

Group-Invariant Max Filtering

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