On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization

DOI10.1137/18M1217644zbMath1427.90234arXiv1809.11083WikidataQ127446453 ScholiaQ127446453MaRDI QIDQ5231691

Afonso S. Bandeira, Shuyang Ling, Ruitu Xu

Publication date: 27 August 2019

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.11083

zbMATH Keywords

nonconvex optimizationdynamical systemKuramoto modeloptimization landscapesynchronization on networks

Mathematics Subject Classification ID

Programming involving graphs or networks (90C35) Nonconvex programming, global optimization (90C26) Stability in context of PDEs (35B35) Synchronization of solutions to ordinary differential equations (34D06)

Related Items (13)

Near-optimal performance bounds for orthogonal and permutation group synchronization via spectral methods ⋮ Improved Performance Guarantees for Orthogonal Group Synchronization via Generalized Power Method ⋮ Solving orthogonal group synchronization via convex and low-rank optimization: tightness and landscape analysis ⋮ Influence of cumulative damage on synchronization of Kuramoto oscillators on networks ⋮ The Kuramoto model on dynamic random graphs ⋮ Max-Cut via Kuramoto-Type Oscillators ⋮ Kuramoto Networks with Infinitely Many Stable Equilibria ⋮ Guarantees for Spontaneous Synchronization on Random Geometric Graphs ⋮ Synchronization of Kuramoto oscillators in dense networks ⋮ The lower bound of the network connectivity guaranteeing in-phase synchronization ⋮ Sufficiently dense Kuramoto networks are globally synchronizing ⋮ Orthogonal Trace-Sum Maximization: Tightness of the Semidefinite Relaxation and Guarantee of Locally Optimal Solutions ⋮ Flow and Elastic Networks on the 𝑛-Torus: Geometry, Analysis, and Computation

Uses Software

• SDPLR

Cites Work

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• Synchronization in complex networks of phase oscillators: a survey
• The Kuramoto model in complex networks
• Tightness of the maximum likelihood semidefinite relaxation for angular synchronization
• User-friendly tail bounds for sums of random matrices
• Chemical oscillations, waves, and turbulence
• Stability of twisted states in the Kuramoto model on Cayley and random graphs
• A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
• From Kuramoto to Crawford: Exploring the onset of synchronization in population of coupled oscillators
• Heuristics for semirandom graph problems
• A geometric analysis of phase retrieval
• Group synchronization on grids
• Local minima and convergence in low-rank semidefinite programming
• Exact matrix completion via convex optimization
• Nonconvex Phase Synchronization
• Guaranteed Matrix Completion via Non-Convex Factorization
• Complete Dictionary Recovery Over the Sphere I: Overview and the Geometric Picture
• Low-Rank Optimization on the Cone of Positive Semidefinite Matrices
• There is no non-zero stable fixed point for dense networks in the homogeneous Kuramoto model
• The size of the sync basin
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• The Projected Power Method: An Efficient Algorithm for Joint Alignment from Pairwise Differences
• Algebraic geometrization of the Kuramoto model: Equilibria and stability analysis
• Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks
• Near-Optimal Bounds for Phase Synchronization
• Bifurcations in the Kuramoto model on graphs
• Message‐Passing Algorithms for Synchronization Problems over Compact Groups
• Synchronization in complex oscillator networks and smart grids
• The non-convex geometry of low-rank matrix optimization
• Exploring complex networks
• How robust are reconstruction thresholds for community detection?
• A Simpler Approach to Matrix Completion

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