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Therefore, the power of the edge server should be controlled to reduce energy consumption. In addition, edge servers with capacitated resources provide services for only a limited number of users to ensure the quality of service (QoS). We set the signal transmission power for the antenna of each edge server and formed a signal disk, ensuring that all users were covered by the edge server signal and minimizing the total power of the system. This scenario is a typical geometric set covering problem, and even simple cases without capacity limits are NP-hard problems. In this paper, we propose a primal\u2013dual-based algorithm and obtain an m-approximation result. We compare our algorithm with two other algorithms through simulation experiments. The results show that our algorithm obtains a result close to the optimal value in polynomial time.<\/jats:p>","DOI":"10.3390\/s22197582","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T05:12:21Z","timestamp":1665378741000},"page":"7582","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Primal\u2013Dual-Based Power Control Approach for Capacitated Edge Servers"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8387-7304","authenticated-orcid":false,"given":"Qinghui","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3094-4347","authenticated-orcid":false,"given":"Weidong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5583-5510","authenticated-orcid":false,"given":"Qian","family":"Su","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6591-0916","authenticated-orcid":false,"given":"Xuejie","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1109\/JIOT.2017.2750180","article-title":"Mobile Edge Computing: A Survey","volume":"5","author":"Abbas","year":"2018","journal-title":"IEEE Internet Things J."},{"key":"ref_2","unstructured":"IEA (2022, September 01). 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