Descent spectral versions of the traditional conjugate gradient
algorithms with application to nonnegative matrix factorization
Fatemeh DARGAHI[1], Saman BABAIE KAFAKI[2],
Zohre AMINIFARD[3]
Abstract. Despite computational superiorities, some
traditional conjugate gradient algorithms such as Polak Ribi re 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, rank-one update, nonnegative matrix factorization.
DOI 10.56082/annalsarsciinfo.2024.1.35
[1] PhD student, Department of Mathematics, Semnan University , Semnan, Iran, (fatemehdargahi@semnan.ac.ir).
[2] Prof., Department of Mathematics, Semnan University , Semnan, Iran, (sbk@semnan.ac.ir).
[3] Senior Researcher, Department of Mathematics, Semnan University , Semnan, Iran (aminisor@semnan.ac.ir).