Space tensor conic programming

Space tensors appear in physics and mechanics. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research area of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive semi-definite space tensors are involved. In thi...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 59; no. 1-2; pp. 307 - 319
Main Authors: Qi, Liqun, Ye, Yinyu
Format: Journal Article
Language:English
Published: Boston Springer US 01.10.2014
Springer Nature B.V
Subjects:
Analysis
Computer science
Conics
Convex analysis
Convex and Discrete Geometry
Diffusion
Eigenvalues
Euclidean space
Linear programming
Magnetic resonance imaging
Management Science
Mathematical analysis
Mathematics
Mathematics and Statistics
NMR
Nuclear magnetic resonance
Operations Research
Operations Research/Decision Theory
Optimization
Programming
Semidefinite programming
Statistics
Studies
Tensors
Three dimensional
Conic linear programming
Duality
Cone
Space tensor
Positive semi-definiteness
Dual cone
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:Space tensors appear in physics and mechanics. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research area of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive semi-definite space tensors are involved. In this short paper, we investigate these problems from the viewpoint of conic linear programming (CLP). We characterize the dual cone of the positive semi-definite space tensor cone, and study the CLP formulation and the duality of positive semi-definite space tensor conic programming.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-013-9577-0