Application of m-weak group inverse in solving optimization problems

Several new expressions are proved for the m -weak group inverse. An effective algorithm for computing m -weak group inverse in terms of the QR decomposition is proposed. Applying the m -weak group inverse, we present the uniquely determined solution to the restricted minimization problem in the Fro...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2024, Vol.118 (1), Article 13
Main Authors: Mosić, Dijana, Stanimirović, Predrag S., Kazakovtsev, Lev A.
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimization
Original Paper
Theoretical
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Summary:Several new expressions are proved for the m -weak group inverse. An effective algorithm for computing m -weak group inverse in terms of the QR decomposition is proposed. Applying the m -weak group inverse, we present the uniquely determined solution to the restricted minimization problem in the Frobenius norm: min ‖ A m + 1 X - A m B ‖ F provided that R ( X ) ⊆ R ( A k ) , where m ∈ N , B ∈ C n × q , A ∈ C n × n and ind ( A ) = k .
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-023-01512-9