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Evaluating the performance for each possible combination is impractical unless [Formula: see text] and [Formula: see text] are small. We relax the original selection problem to be a convex optimization problem and describe a projected gradient method with Barzilai\u2013Borwein step size to solve the proposed relaxed problem. Numerical results demonstrate that the proposed algorithm converges faster than some classical algorithms. The solution obtained by the proposed algorithm is closer to the truth. <\/jats:p>","DOI":"10.1177\/1550147719839642","type":"journal-article","created":{"date-parts":[[2019,3,28]],"date-time":"2019-03-28T12:53:25Z","timestamp":1553777605000},"page":"155014771983964","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["New gradient methods for sensor selection problems"],"prefix":"10.1177","volume":"15","author":[{"given":"De","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China"},{"name":"Information Science Academy, China Electronics Technology Group Corporation, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6308-5062","authenticated-orcid":false,"given":"Mingqiang","family":"Li","sequence":"additional","affiliation":[{"name":"Information 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