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Based on the BB stepsize technique, we design a nonmonotonic descent stepsize and then derive a new gradient projection algorithm to solve this problem. The convergence analysis of the new gradient projected algorithm is given. Some numerical examples show that the new method is feasible and effective. Especially, some simulation experiments in the color image restoration problems illustrate that our algorithm is more effective than the existed algorithms.<\/jats:p>","DOI":"10.1002\/nla.2385","type":"journal-article","created":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T06:54:20Z","timestamp":1619074460000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An efficient algorithm for solving the nonnegative tensor least squares problem"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-3326-4585","authenticated-orcid":false,"given":"Xue\u2010Feng","family":"Duan","sequence":"first","affiliation":[{"name":"College of Mathematics and Computational Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin P.R. 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