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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Convex Optimization of Graph Laplacian Eigenvalues canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4539862 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Convex Optimization of Graph Laplacian Eigenvalues Context triple: [Stephen P. Boyd, notableWork, Convex Optimization of Graph Laplacian Eigenvalues]
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A.
Laplacian spectrum
The Laplacian spectrum is the collection of eigenvalues of the Laplace operator on a domain or manifold, encoding how functions vibrate or diffuse over it and serving as a key tool in spectral geometry and mathematical physics.
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B.
Nonlinear programming
Nonlinear programming is a branch of mathematical optimization focused on finding optimal solutions to problems where the objective function or constraints are nonlinear.
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C.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
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D.
The Convexity of Hilltops
"The Convexity of Hilltops" is a seminal geomorphological study by American geologist Grove Karl Gilbert that analyzes the shapes and formation processes of hilltops in relation to erosion and landscape evolution.
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E.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Convex Optimization of Graph Laplacian Eigenvalues Target entity description: "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.
-
A.
Laplacian spectrum
The Laplacian spectrum is the collection of eigenvalues of the Laplace operator on a domain or manifold, encoding how functions vibrate or diffuse over it and serving as a key tool in spectral geometry and mathematical physics.
-
B.
Nonlinear programming
Nonlinear programming is a branch of mathematical optimization focused on finding optimal solutions to problems where the objective function or constraints are nonlinear.
-
C.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
-
D.
The Convexity of Hilltops
"The Convexity of Hilltops" is a seminal geomorphological study by American geologist Grove Karl Gilbert that analyzes the shapes and formation processes of hilltops in relation to erosion and landscape evolution.
-
E.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Convex Optimization of Graph Laplacian Eigenvalues Description of subject: "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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.