{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T09:20:58Z","timestamp":1648891258694},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2017,9,18]],"date-time":"2017-09-18T00:00:00Z","timestamp":1505692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/about_us\/legal\/notices"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,6,1]]},"DOI":"10.1093\/comjnl\/bxx085","type":"journal-article","created":{"date-parts":[[2017,8,24]],"date-time":"2017-08-24T15:13:37Z","timestamp":1503587617000},"page":"798-807","source":"Crossref","is-referenced-by-count":3,"title":["On Handelman\u2019s Representation of Network Utility Maximization"],"prefix":"10.1093","volume":"61","author":[{"given":"Tua A","family":"Tamba","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Industrial Technology, Parahyangan Catholic University, Bandung 40141, Indonesia"}]}],"member":"286","published-online":{"date-parts":[[2017,9,18]]},"reference":[{"key":"key\n\t\t\t\t20180601110931_bxx085C1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1002\/ett.4460080106","article-title":"Charging and rate control for elastic traffic","volume":"8","author":"Kelly","year":"1997","journal-title":"Eur. T. Telecommun."},{"key":"key\n\t\t\t\t20180601110931_bxx085C2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1057\/palgrave.jors.2600523","article-title":"Rate control for communication networks: shadow prices, proportional fairness and stability","volume":"49","author":"Kelly","year":"1998","journal-title":"J. Oper. Res. Soc."},{"key":"key\n\t\t\t\t20180601110931_bxx085C3","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1109\/JSAC.2006.879350","article-title":"A tutorial on decomposition methods for network utility maximization","volume":"24","author":"Palomar","year":"2006","journal-title":"IEEE J. Sel. Area Comm."},{"key":"key\n\t\t\t\t20180601110931_bxx085C4","doi-asserted-by":"crossref","first-page":"2254","DOI":"10.1109\/TAC.2007.910665","article-title":"Alternative distributed algorithms for network utility maximization: Framework and applications","volume":"52","author":"Palomar","year":"2007","journal-title":"IEEE T. Automat. Contr."},{"key":"key\n\t\t\t\t20180601110931_bxx085C5","author":"Fazel","year":"2005"},{"key":"key\n\t\t\t\t20180601110931_bxx085C6","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/978-0-387-75714-8_5","volume-title":"Advances in Applied Mathematics and Global Optimization","author":"Chiang","year":"2009"},{"key":"key\n\t\t\t\t20180601110931_bxx085C7","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1109\/TNET.2007.896507","article-title":"Distributed rate allocation for inelastic flows","volume":"15","author":"Hande","year":"2007","journal-title":"IEEE ACM T. Netw."},{"key":"key\n\t\t\t\t20180601110931_bxx085C8","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1109\/TVT.2014.2331213","article-title":"Resource allocation for semi-elastic applications with outage constraints in cellular networks","volume":"64","author":"Yang","year":"2015","journal-title":"IEEE T. Veh. Technol."},{"key":"key\n\t\t\t\t20180601110931_bxx085C9","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1109\/49.414637","article-title":"Fundamental design issues for the future internet","volume":"13","author":"Shenker","year":"1995","journal-title":"IEEE J. Sel. Area Comm."},{"key":"key\n\t\t\t\t20180601110931_bxx085C10","first-page":"144","author":"Nguyen-Vuong","year":"2008"},{"key":"key\n\t\t\t\t20180601110931_bxx085C11","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1109\/TNET.2005.852876","article-title":"Non-convex optimization and rate control for multi-class services in the internet","volume":"13","author":"Lee","year":"2005","journal-title":"IEEE ACM T. Netw."},{"key":"key\n\t\t\t\t20180601110931_bxx085C12","doi-asserted-by":"crossref","first-page":"35","DOI":"10.2140\/pjm.1988.132.35","article-title":"Representing polynomials by positive linear functions on compact convex polyhedra","volume":"132","author":"Handelman","year":"1988","journal-title":"Pac. J. Math."},{"key":"key\n\t\t\t\t20180601110931_bxx085C13","first-page":"576","author":"Sankaranarayanan","year":"2013"},{"key":"key\n\t\t\t\t20180601110931_bxx085C14","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1093\/imamci\/dnv003","article-title":"Linear relaxations of polynomial positivity for polynomial lyapunov function synthesis","volume":"33","author":"Ben Sassi","year":"2016","journal-title":"IMA J. Math. Control I."},{"key":"key\n\t\t\t\t20180601110931_bxx085C15","doi-asserted-by":"crossref","first-page":"2383","DOI":"10.3934\/dcdsb.2015.20.2383","article-title":"Polynomial optimization with applications to stability analysis and control - alternatives to sum of squares","volume":"20","author":"Kamyar","year":"2015","journal-title":"Discret. Contin. Dyn. S."},{"key":"key\n\t\t\t\t20180601110931_bxx085C16","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1016\/j.automatica.2011.01.012","article-title":"Robust stability and instability of biochemical networks with parametric uncertainty","volume":"47","author":"Waldherr","year":"2011","journal-title":"Automatica"},{"key":"key\n\t\t\t\t20180601110931_bxx085C17","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1287\/moor.27.2.347.322","article-title":"Semidefinite programming vs. lp relaxations for polynomial programming","volume":"27","author":"Lasserre","year":"2002","journal-title":"Math. Oper. Res."},{"key":"key\n\t\t\t\t20180601110931_bxx085C18","doi-asserted-by":"crossref","first-page":"3104","DOI":"10.1137\/100790835","article-title":"Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube","volume":"20","author":"De Klerk","year":"2010","journal-title":"SIAM J. Optimiz."},{"key":"key\n\t\t\t\t20180601110931_bxx085C19","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-35651-8","volume-title":"Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra","author":"Cox","year":"2007"},{"key":"key\n\t\t\t\t20180601110931_bxx085C20","first-page":"83","volume-title":"Algorithmic and Quantitative Real Algebraic Geometry, DIMACS Series in Discrete Mathematics and Theoretical Computer Science","author":"Parrilo","year":"2003"},{"key":"key\n\t\t\t\t20180601110931_bxx085C21","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s10107-003-0387-5","article-title":"Semidefinite programming relaxations for semialgebraic problems","volume":"96","author":"Parrilo","year":"2003","journal-title":"Math. Program."},{"key":"key\n\t\t\t\t20180601110931_bxx085C22","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/978-0-387-09686-5_7","volume-title":"Emerging Applications of Algebraic Geometry","author":"Laurent","year":"2009"},{"key":"key\n\t\t\t\t20180601110931_bxx085C23","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1137\/S1052623400366802","article-title":"Global optimization with polynomials and the problem of moments","volume":"11","author":"Lasserre","year":"2001","journal-title":"SIAM J. Optimiz."},{"key":"key\n\t\t\t\t20180601110931_bxx085C24","volume-title":"Semidefinite Optimization and Convex Algebraic Geometry","author":"Blekherman","year":"2013"},{"key":"key\n\t\t\t\t20180601110931_bxx085C25","author":"Tamba","year":"2013"},{"key":"key\n\t\t\t\t20180601110931_bxx085C26","author":"Tamba","year":"2014"},{"key":"key\n\t\t\t\t20180601110931_bxx085C27","author":"Tamba","year":"2014"},{"key":"key\n\t\t\t\t20180601110931_bxx085C28","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF01362149","article-title":"A nullstellensatz and a positivstellensatz in semialgebraic geometry","volume":"207","author":"Stengle","year":"1974","journal-title":"Math. Ann."},{"key":"key\n\t\t\t\t20180601110931_bxx085C29","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"Boyd","year":"2004"},{"key":"key\n\t\t\t\t20180601110931_bxx085C30","volume-title":"Computing in Algebraic Geometry, Algorithms and Computation in Mathematics","author":"Decker","year":"2006"},{"key":"key\n\t\t\t\t20180601110931_bxx085C31","author":"Decker","year":"2012"},{"key":"key\n\t\t\t\t20180601110931_bxx085C32","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.jsc.2005.09.007","article-title":"Bruno buchberger\u2019sphd thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal","volume":"41","author":"Buchberger","year":"2006","journal-title":"J. Symb. Comput."},{"key":"key\n\t\t\t\t20180601110931_bxx085C33","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/S0747-7171(08)80086-7","article-title":"Solving zero-dimensional algebraic systems","volume":"13","author":"Lazard","year":"1992","journal-title":"J. Symb. Comput."},{"key":"key\n\t\t\t\t20180601110931_bxx085C34","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BF01200146","article-title":"On decomposing systems of polynomial equations with finitely many solutions","volume":"4","author":"M\u00f6ller","year":"1993","journal-title":"Appl. Algebr. Eng. Comm."},{"key":"key\n\t\t\t\t20180601110931_bxx085C35","author":"Mosek","year":"2010"},{"key":"key\n\t\t\t\t20180601110931_bxx085C36","author":"Prajna","year":"2004"},{"key":"key\n\t\t\t\t20180601110931_bxx085C37","first-page":"829","author":"Bickson","year":"2009"},{"key":"key\n\t\t\t\t20180601110931_bxx085C38","first-page":"143","author":"Tamba","year":"2016"},{"key":"key\n\t\t\t\t20180601110931_bxx085C39","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.jpaa.2003.12.011","article-title":"Symmetry groups, semidefinite programs, and sums of squares","volume":"192","author":"Gatermann","year":"2004","journal-title":"J. Pure. Appl. Algebra"},{"key":"key\n\t\t\t\t20180601110931_bxx085C40","first-page":"1871","author":"Permenter","year":"2012"},{"key":"key\n\t\t\t\t20180601110931_bxx085C41","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1109\/TAC.2009.2017144","article-title":"Pre-and post-processing sum-of-squares programs in practice","volume":"54","author":"Lofberg","year":"2009","journal-title":"IEEE T. Automat. Contr."},{"key":"key\n\t\t\t\t20180601110931_bxx085C42","author":"Permenter","year":"2014"},{"key":"key\n\t\t\t\t20180601110931_bxx085C43","author":"Ahmadi","year":"2014"}],"container-title":["The Computer Journal"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/comjnl\/article-pdf\/61\/6\/798\/24978967\/bxx085.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,2]],"date-time":"2019-10-02T15:45:25Z","timestamp":1570031125000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comjnl\/article\/61\/6\/798\/4160674"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,18]]},"references-count":43,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2017,9,18]]},"published-print":{"date-parts":[[2018,6,1]]}},"URL":"https:\/\/doi.org\/10.1093\/comjnl\/bxx085","relation":{},"ISSN":["0010-4620","1460-2067"],"issn-type":[{"value":"0010-4620","type":"print"},{"value":"1460-2067","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2018,6]]},"published":{"date-parts":[[2017,9,18]]}}}