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Specifically, it revisits the solution to the energy efficiency (EE) problem using the alternating optimization (AO) approach. In each AO iteration, the RIS phase optimization is achieved using the gradient descent method, which unfortunately does not guarantee convergence. To overcome this limitation, we propose two alternatives: the Wolfe-based gradient-descent (GAW) EE maximization Algorithm and the trust region (TR)-based EE maximization algorithm. Additionally, we use Dinkelbach\u2019s algorithm to obtain the optimal transmit power allocation. Our results demonstrate that the proposed methods outperform the existing approach that uses sequential fractional programming (SFP) for phase optimization and the traditional relay-based method.<\/jats:p>","DOI":"10.1186\/s13638-023-02296-7","type":"journal-article","created":{"date-parts":[[2023,9,5]],"date-time":"2023-09-05T01:01:26Z","timestamp":1693875686000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Energy efficient resource allocation for re-configurable intelligent surface-assisted wireless networks"],"prefix":"10.1186","volume":"2023","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3235-5629","authenticated-orcid":false,"given":"Samaneh","family":"Bidabadi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Messaoud","family":"Ahmed Ouameur","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miloud","family":"Bagaa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Massicotte","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,5]]},"reference":[{"key":"2296_CR1","unstructured":"N. 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