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Using a new regularized factorization method for unconstrained optimization problems
Author(s) -
Dehghan Niri Tayebeh,
Shahzadeh Fazeli Seyed Abolfazl,
Hosseini Mohammad Mehdi
Publication year - 2019
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2580
Subject(s) - incomplete cholesky factorization , cholesky decomposition , hessian matrix , incomplete lu factorization , factorization , dixon's factorization method , convergence (economics) , mathematical optimization , minimum degree algorithm , computer science , matrix decomposition , mathematics , positive definite matrix , algorithm , eigenvalues and eigenvectors , physics , quantum mechanics , economics , economic growth
In this paper, a new regularized factorization method is presented for solving unconstrained minimization problems in which the Hessian matrix may not be a positive definite or may be close to singular. With employing the modified quadrant interlocking factorization (QIF), an efficient algorithm is developed to find a suitable method. Moreover, under suitable conditions, the global convergence of the proposed method is established. Some interesting examples are solved by the proposed method and the improved Cholesky factorization method. The results show that the proposed method, in the most cases, the algorithm has a faster convergence than the improved Cholesky factorization method.