An interior-point algorithm for linearly constrained convex optimization based on kernel function and application in non-negative matrix factorization

In this paper, an interior point method (IPM) based on a new kernel function for solving linearly constrained convex optimization problems is presented. So, firstly a survey on several trigonometric kernel functions defined in literature is done and some properties of them are studied. Then some com...

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Veröffentlicht in:Optimization and engineering Jg. 21; H. 3; S. 1019 - 1051
Hauptverfasser: Fathi-Hafshejani, S., Moaberfard, Z.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2020
Springer Nature B.V
Schlagworte:
Algorithms
Computational geometry
Control
Convex analysis
Convexity
Engineering
Environmental Management
Factorization
Financial Engineering
Iterative methods
Kernel functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Research Article
Systems Theory
Large-update methods
Kernel function
Interior point methods
Complexity bounds
Linearly constrained convex optimization
Non-negative matrix factorization
ISSN:1389-4420, 1573-2924
Online-Zugang:Volltext
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Zusammenfassung:In this paper, an interior point method (IPM) based on a new kernel function for solving linearly constrained convex optimization problems is presented. So, firstly a survey on several trigonometric kernel functions defined in literature is done and some properties of them are studied. Then some common characteristics of these functions which help us to define a new trigonometric kernel function are obtained. We generalize the growth term of the kernel function by applying a positive parameter p and rewritten the trigonometric kernel functions defined in the literature. By the help of some simple analysis tools, we show that the IPM based on the new kernel function obtains O n log n log n ϵ iteration complexity bound for large-update methods. Finally, we illustrate some numerical results of performing IPMs based on the kernel functions for solving non-negative matrix factorization problems.
Bibliographie:ObjectType-Article-1
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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-020-09514-x