Exploiting aggregate sparsity in second-order cone relaxations for quadratic constrained quadratic programming problems

Sheen, Heejune; Yamashita, Makoto

doi:10.1080/10556788.2020.1827256

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…( 23). Exploiting such sparsity may reduce the computational complexity of solving the equivalent SOCP for our CSpeC framework 70 . The other steps of SilenceMap have lower degrees of polynomial time complexity (e.g., the least-square solution in Eq.…”

Section: And ζ I Are Regularization Parameters Andmentioning

confidence: 99%

Neural silences can be localized rapidly using noninvasive scalp EEG

2021

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A rapid and cost-effective noninvasive tool to detect and characterize neural silences can be of important benefit in diagnosing and treating many disorders. We propose an algorithm, SilenceMap, for uncovering the absence of electrophysiological signals, or neural silences, using noninvasive scalp electroencephalography (EEG) signals. By accounting for the contributions of different sources to the power of the recorded signals, and using a hemispheric baseline approach and a convex spectral clustering framework, SilenceMap permits rapid detection and localization of regions of silence in the brain using a relatively small amount of EEG data. SilenceMap substantially outperformed existing source localization algorithms in estimating the center-of-mass of the silence for three pediatric cortical resection patients, using fewer than 3 minutes of EEG recordings (13, 2, and 11mm vs. 25, 62, and 53 mm), as well for 100 different simulated regions of silence based on a real human head model (12 ± 0.7 mm vs. 54 ± 2.2 mm). SilenceMap paves the way towards accessible early diagnosis and continuous monitoring of altered physiological properties of human cortical function.

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Section: And ζ I Are Regularization Parameters Andmentioning

confidence: 99%

Neural silences can be localized rapidly using noninvasive scalp EEG

2021

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“…In this case, the exact optimal solution and exact optimal value can be computed in polynomial time. A secondorder cone programming (SOCP) relaxation can be obtained by further relaxing the positive semidefinite constraint X O, for instance, requiring all 2 × 2 principal submatrices of X to be positive semidefinite [11,20]. For QCQPs with a certain sparsity structure, e.g., forest structures, the SDP relaxation coincides with the SOCP relaxation.…”

Section: Introductionmentioning

confidence: 99%

Exact SDP relaxations for quadratic programs with bipartite graph structures

Azuma¹,

Fukuda²,

Kim³

et al. 2022

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For nonconvex quadratically constrained quadratic programs (QCQPs), we first show that, under certain feasibility conditions, the standard semidefinite (SDP) relaxation is exact for QCQPs with bipartite graph structures. The exact optimal solutions are obtained by examining the dual SDP relaxation and the rank of the optimal solution of this dual SDP relaxation under strong duality. Our results on the QCQPs generalize the results on QCQP with sign-definite bipartite graph structures, QCQPs with forest structures, and QCQPs with nonpositive off-diagonal data elements. Second, we propose a conversion method from QCQPs with no particular structure to the ones with bipartite graph structures. As a result, we demonstrate that a wider class of QCQPs can be exactly solved by the SDP relaxation. Numerical instances are presented for illustration.

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