Convex Optimization of Graph Laplacian Eigenvalues
E451069
"Convex Optimization of Graph Laplacian Eigenvalues" is a research work by Stephen P. Boyd that develops convex optimization methods to analyze and design graphs via the spectral properties of their Laplacian matrices.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
research work
ⓘ
scientific paper ⓘ |
| aimsTo |
improve graph connectivity via optimization
ⓘ
optimize eigenvalues of graph Laplacians ⓘ provide convex formulations for spectral graph problems ⓘ |
| appliesTo |
network design problems
ⓘ
undirected graphs ⓘ weighted graphs ⓘ |
| assumes | Laplacian matrix is symmetric and positive semidefinite ⓘ |
| author | Stephen P. Boyd NERFINISHED ⓘ |
| basedOn |
convex analysis
ⓘ
matrix analysis ⓘ properties of symmetric matrices ⓘ |
| characterizes |
convex sets defined by Laplacian eigenvalue constraints
ⓘ
trade-offs between graph sparsity and connectivity ⓘ |
| contributesTo |
graph design methodologies
ⓘ
optimization-based network design ⓘ spectral optimization of graphs ⓘ |
| field |
applied mathematics
ⓘ
convex optimization ⓘ graph theory ⓘ spectral graph theory ⓘ |
| focusesOn |
analysis of graphs via spectral properties
ⓘ
design of graphs via spectral properties ⓘ graph Laplacian eigenvalues ⓘ |
| hasApplicationIn |
communication networks
ⓘ
power networks ⓘ sensor networks ⓘ social network analysis ⓘ |
| language | English ⓘ |
| provides |
design rules for graph weights
ⓘ
examples of convex graph design problems ⓘ optimization formulations for eigenvalue bounds ⓘ |
| relatedTo |
algebraic connectivity maximization
ⓘ
control of networked systems ⓘ distributed algorithms on graphs ⓘ robust network design ⓘ spectral clustering ⓘ |
| studies |
Laplacian matrix of a graph
ⓘ
algebraic connectivity of graphs ⓘ graph connectivity measures ⓘ second smallest Laplacian eigenvalue ⓘ spectral properties of graph Laplacians ⓘ |
| usesMethod |
convex optimization
ⓘ
eigenvalue optimization ⓘ semidefinite programming ⓘ |
Referenced by (1)
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