Fatemeh DARGAHI1, Saman BABAIE–KAFAKI2, Zohre AMINIFARD3
Abstract. Despite computational superiorities, some traditional conjugate gradient algorithms such as Polak–Ribiére–Polyak and Hestenes–Stiefel methods generally fail to guarantee the descent condition. Here, in a matrix viewpoint, spectral versions of such methods are developed which fulfill the descent condition. The convergence of the given spectral algorithms is argued briefly. Afterwards, we propose an improved version of the nonnegative matrix factorization problem by adding penalty terms to the model, for controlling the condition number of one of the factorization elements. Finally, the computational merits of the method are examined using a set of CUTEr test problems as well as some random nonnegative matrix factorization models. The results typically agree with our analytical spectrum.
Keywords: Unconstrained optimization, conjugate gradient method, spectral method, rankone update, nonnegative matrix factorization.
DOI 10.56082/annalsarsciinfo.2024.1.35
1PhD student, Department of Mathematics, “Semnan University”, Semnan, Iran, (fatemehdargahi@semnan.ac.ir).
2Prof., Department of Mathematics, “Semnan University”, Semnan, Iran, (sbk@semnan.ac.ir).
3Senior Researcher, Department of Mathematics, “Semnan University”, Semnan, Iran (aminisor@semnan.ac.ir).
PUBLISHED in Annals of the Academy of Romanian Scientists Series on Science and Technology of Information, Volume 17, No1
ISSN PRINT2066 – 2742 ISSN ONLINE 2066-8562 
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