{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T19:12:22Z","timestamp":1774897942103,"version":"3.50.1"},"reference-count":62,"publisher":"Emerald","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,1,1]]},"abstract":"<jats:p>We consider a network of devices, such as generators, fixed loads, deferrable loads, and storage devices, each with its own dynamic constraints and objective, connected by AC and DC lines. The problem is to minimize the total network objective subject to the device and line constraints over a time horizon. This is a large optimization problem with variables for consumption or generation for each device, power flow for each line, and voltage phase angles at AC buses in each period.<\/jats:p>\n                  <jats:p>We develop a decentralized method for solving this problem called proximal message passing. The method is iterative: At each step, every device exchanges simple messages with its neighbors in the network and then solves its own optimization problem, minimizing its own objective augmented by a term determined by the messages it has received. We show that this message passing method converges to a solution when the device objective and constraints are convex. The method is completely decentralized and needs no global coordination other than iteration synchronization; the problems to be solved by each device can typically be solved extremely efficiently and in parallel.<\/jats:p>\n                  <jats:p>The proximal message passing method is fast enough that even a serial implementation can solve substantial problems in reasonable time frames. We report results for several numerical experiments, demonstrating the method\u2019s speed and scaling, including the solution of a problem instance with over 30 million variables in 5 minutes for a serial implementation; with decentralized computing, the solve time would be less than one second.<\/jats:p>","DOI":"10.1561\/2400000002","type":"journal-article","created":{"date-parts":[[2013,12,30]],"date-time":"2013-12-30T11:19:32Z","timestamp":1388402372000},"page":"73-126","source":"Crossref","is-referenced-by-count":156,"title":["Dynamic Network Energy Management via Proximal Message Passing"],"prefix":"10.1561","volume":"1","author":[{"given":"Matt","family":"Kraning","sequence":"first","affiliation":[{"name":"Stanford University"}]},{"given":"Eric","family":"Chu","sequence":"additional","affiliation":[{"name":"Stanford University"}]},{"given":"Javad","family":"Lavaei","sequence":"additional","affiliation":[{"name":"Columbia University"}]},{"given":"Stephen","family":"Boyd","sequence":"additional","affiliation":[{"name":"Stanford University"}]}],"member":"140","published-online":{"date-parts":[[2014,1,1]]},"reference":[{"key":"2026033014320076200_ref001","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511610868","volume-title":"Applied Optimization: Formulation and Algorithms for Engineering Systems","author":"Baldick","year":"2006"},{"key":"2026033014320076200_ref002","article-title":"Decomposition methods for large scale LP decoding","volume-title":"Submitted, IEEE Transactions on Information Theory","author":"Barman","year":"2012"},{"key":"2026033014320076200_ref003","first-page":"6678","volume-title":"Model predictive control design: New trends and tools","author":"Bemporad","year":"2006"},{"key":"2026033014320076200_ref004","volume-title":"Power Systems Analysis","author":"Bergen","year":"1999"},{"key":"2026033014320076200_ref005","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","author":"Bertsekas","year":"1982"},{"key":"2026033014320076200_ref006","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed optimization and statistical learning via the alternating direction method of multipliers","volume":"3","author":"Boyd","year":"2011","journal-title":"Foundations and Trends in Machine Learning"},{"key":"2026033014320076200_ref007","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"Boyd","year":"2004"},{"issue":"8","key":"2026033014320076200_ref008","first-page":"431","article-title":"Contribution to the economic dispatch problem","volume":"3","author":"Carpentier","year":"1962","journal-title":"Bull. Soc. Francaise Elect."},{"key":"2026033014320076200_ref009","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-1605-0","volume-title":"Control & Optimization Methods for Electric Smart Grids","author":"Chakrabortty","year":"2012"},{"key":"2026033014320076200_ref010","first-page":"255","volume-title":"Layering as optimization decomposition: A mathematical theory of network architectures","author":"Chiang","year":"2007"},{"key":"2026033014320076200_ref011","first-page":"1409","volume-title":"Supply chain planning: Rolling horizon scheduling of multi-factory supply chains","author":"Cho","year":"2003"},{"issue":"4","key":"2026033014320076200_ref012","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.1109\/59.99376","article-title":"A review of recent advances in economic dispatch","volume":"5","author":"Chowdhury","year":"1990","journal-title":"IEEE Transactions on Power Systems"},{"key":"2026033014320076200_ref013","first-page":"401","volume-title":"Seasonal energy storage in a renewable energy system","author":"Converse","year":"2012"},{"key":"2026033014320076200_ref014","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1287\/opre.8.1.101","article-title":"Decomposition principle for linear programs","volume":"8","author":"Dantzig","year":"1960","journal-title":"Operations Research"},{"issue":"1","key":"2026033014320076200_ref015","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BF02196592","article-title":"Parallel alternating direction multiplier decomposition of convex programs","volume":"80","author":"Eckstein","year":"1994","journal-title":"Journal of Optimization Theory and Applications"},{"key":"2026033014320076200_ref016","unstructured":"J. H.\n              Eto\n             and R. J.Thomas. Computational needs for the next generation electric grid. In Department of Energy, 2011. http:\/\/certs.lbl.gov\/pdf\/lbnl-5105e.pdf."},{"issue":"3","key":"2026033014320076200_ref017","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1287\/opre.11.3.399","article-title":"Generalized Lagrange multiplier method for solving problems of optimum allocation of resources","volume":"11","author":"Everett","year":"1963","journal-title":"Operations Research"},{"key":"2026033014320076200_ref018","volume-title":"Energy and Power Risk Management: New Developments in Modeling, Pricing and Hedging","author":"Eydeland","year":"2002"},{"issue":"2","key":"2026033014320076200_ref019","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/18.910573","article-title":"Codes of graphs: Normal realizations","volume":"47","author":"Forney","year":"2001","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026033014320076200_ref020","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0898-1221(76)90003-1","article-title":"A dual algorithm for the solution of nonlinear variational problems via finite element approximations","volume":"2","author":"Gabay","year":"1976","journal-title":"Computers and Mathematics with Applications"},{"key":"2026033014320076200_ref021","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1051\/m2an\/197509R200411","article-title":"Sur l\u2019approximation, par elements finis d\u2019ordre un, et la resolution, par penalisation-dualit\u00e9, d\u2019une classe de problems de Dirichlet non-lineares","volume":"9","author":"Glowinski","year":"1975","journal-title":"Revue Fran\u00e7aise d\u2019Automatique, Informatique, et Recherche Op\u00e9rationelle"},{"issue":"3","key":"2026033014320076200_ref022","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1109\/T-PAS.1977.32397","article-title":"Optimal power dispatch \u2014 a comprehensive survey","volume":"96","author":"Happ","year":"1977","journal-title":"IEEE Transactions on Power Apparatus and Systems"},{"key":"2026033014320076200_ref023","first-page":"322","volume-title":"The potential of intermittent renewables to meet electric power demand: current methods and emerging analytical techniques","author":"Hart","year":"2012"},{"key":"2026033014320076200_ref024","volume-title":"Strategic Portfolio Management for Long-Term Investments: An Optimal Control Approach","author":"Herzog","year":"2005"},{"key":"2026033014320076200_ref025","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/BF00927673","article-title":"Multiplier and gradient methods","volume":"4","author":"Hestenes","year":"1969","journal-title":"Journal of Optimization Theory and Applications"},{"key":"2026033014320076200_ref026","first-page":"1","volume-title":"Energy storage in power system operation: The power nodes modeling framework","author":"Heussen","year":"2010"},{"issue":"8","key":"2026033014320076200_ref027","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1080\/00207179.2012.742207","article-title":"Nonconvex model predictive control for commercial refrigeration","volume":"86","author":"Hovgaard","year":"2013","journal-title":"International Journal of Control"},{"issue":"4","key":"2026033014320076200_ref028","doi-asserted-by":"crossref","first-page":"1875","DOI":"10.1109\/TPWRS.2011.2129542","article-title":"Efficient coordination of wind power and price-responsive demand \u2014 Part I: Theoretical foundations","volume":"26","author":"Ilic","year":"2011","journal-title":"IEEE Transactions on Power Systems"},{"issue":"4","key":"2026033014320076200_ref029","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1109\/TPWRS.2011.2129543","article-title":"Efficient coordination of wind power and price-responsive demand\u2014part ii: Case studies","volume":"26","author":"Ilic","year":"2011","journal-title":"IEEE Transactions on Power Systems"},{"key":"2026033014320076200_ref030","article-title":"Embedded online optimization for model predictive control at megahertz rates","volume-title":"Submitted, IEEE Transactions on Automatic Control","author":"Jerez","year":"2013"},{"key":"2026033014320076200_ref031","doi-asserted-by":"crossref","DOI":"10.1109\/NAPS.2012.6336364","volume-title":"Joint power system state estimation and breaker status identification","author":"Kekatos","year":"2012"},{"key":"2026033014320076200_ref032","doi-asserted-by":"crossref","DOI":"10.1109\/TPWRS.2012.2219629","article-title":"Distributed robust power system state estimation","volume-title":"IEEE Transactions on Power Systems","author":"Kekatos","year":"2013"},{"key":"2026033014320076200_ref033","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1057\/palgrave.jors.2600523","article-title":"Rate control in communication networks: shadow prices, proportional fairness and stability","volume":"49","author":"Kelly","year":"1998","journal-title":"Journal of the Operational Research Society"},{"key":"2026033014320076200_ref034","first-page":"87","volume-title":"Control and Optimization Methods for Electric Smart Grids, volume 3 of Power Electronics and Power Systems","author":"Kiana","year":"2012"},{"issue":"2","key":"2026033014320076200_ref035","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1109\/59.589777","article-title":"Coarse-grained distributed optimal power flow","volume":"12","author":"Kim","year":"1997","journal-title":"IEEE Transactions on Power Systems"},{"issue":"2","key":"2026033014320076200_ref036","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1109\/59.867147","article-title":"A comparison of distributed optimal power flow algorithms","volume":"15","author":"Kim","year":"2000","journal-title":"IEEE Transactions on Power Systems"},{"key":"2026033014320076200_ref037","first-page":"10487","volume-title":"Operation and configuration of a storage portfolio via convex optimization","author":"Kraning","year":"2011"},{"key":"2026033014320076200_ref038","unstructured":"A.\n              Lam\n            , B.Zhang, and D.Tse. Distributed algorithms for optimal power flow problem. http:\/\/arxiv.org\/abs\/1109.5229, 2011."},{"issue":"1","key":"2026033014320076200_ref039","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TPWRS.2011.2160974","article-title":"Zero duality gap in optimal power flow problem","volume":"27","author":"Lavaei","year":"2012","journal-title":"IEEE Transactions on Power Systems"},{"key":"2026033014320076200_ref040","doi-asserted-by":"crossref","DOI":"10.1109\/PESGM.2012.6344803","volume-title":"Geometry of power flows in tree networks","author":"Lavaei","year":"2012"},{"key":"2026033014320076200_ref041","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1109\/TSG.2011.2174068","article-title":"Wide-area measurement based dynamic stochastic optimal power flow control for smart grids with high variability and uncertainty","volume":"3","author":"Liang","year":"2012","journal-title":"IEEE Transactions on Smart Grid"},{"key":"2026033014320076200_ref042","first-page":"226","volume-title":"Understanding tcp vegas: a duality model","author":"Low","year":"2001"},{"key":"2026033014320076200_ref043","volume-title":"Predictive Control with Constraints","author":"Maciejowski","year":"2002"},{"key":"2026033014320076200_ref044","first-page":"335","volume-title":"How thermal energy storage enhances the economic viability of concentrating solar power","author":"Madaeni","year":"2012"},{"key":"2026033014320076200_ref045","first-page":"135","volume-title":"Pregel: A system for large-scale graph processing","author":"Malewicz","year":"2010"},{"key":"2026033014320076200_ref046","unstructured":"J.\n              Mattingley\n             and S.Boyd. CVXGEN: Automatic convex optimization code generation. http:\/\/cvxgen.com\/, 2012."},{"key":"2026033014320076200_ref047","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1109\/MCS.2011.940571","article-title":"Receding horizon control: Automatic generation of high-speed solvers","volume":"31","author":"Mattingley","year":"2011","journal-title":"IEEE Control Systems Magazine"},{"key":"2026033014320076200_ref048","first-page":"473","volume-title":"The history, present state, and future prospects of underground pumped hydro for massive energy storage","author":"Pickard","year":"2012"},{"key":"2026033014320076200_ref049","volume-title":"Optimization","author":"Powell","year":"1969"},{"issue":"7","key":"2026033014320076200_ref050","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1016\/S0967-0661(02)00186-7","article-title":"A survey of industrial model predictive control technology","volume":"11","author":"Qin","year":"2003","journal-title":"Control Engineering Practice"},{"key":"2026033014320076200_ref051","first-page":"1043","article-title":"Message-passing for graph-structured linear programs: Proximal methods and rounding schemes","volume":"11","author":"Ravikumar","year":"2010","journal-title":"Journal of Machine Learning Research"},{"key":"2026033014320076200_ref052","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"Rockafellar","year":"1970"},{"issue":"2","key":"2026033014320076200_ref053","first-page":"1","article-title":"Gossip algorithms","volume":"3","author":"Shah","year":"2008","journal-title":"Foundations and Trends in Networking"},{"key":"2026033014320076200_ref054","doi-asserted-by":"crossref","DOI":"10.1109\/PESGM.2012.6345272","volume-title":"Physics of power networks makes hard problems easy to solve","author":"Sojoudi","year":"2012"},{"key":"2026033014320076200_ref055","doi-asserted-by":"crossref","unstructured":"S.\n              Sojoudi\n             and J.Lavaei. Convexification of generalized network flow problem with application to power systems. Preprint available athttp:\/\/www.ee.columbia.edu\/~lavaei\/Generalized_Net_Flow.pdf, 2013.","DOI":"10.1109\/CDC.2013.6761089"},{"key":"2026033014320076200_ref056","doi-asserted-by":"crossref","unstructured":"S.\n              Sojoudi\n             and J.Lavaei. Semidefinite relaxation for nonlinear optimization over graphs with application to power systems. Preprint available athttp:\/\/www.ee.columbia.edu\/~lavaei\/Opt_Over_Graph.pdf, 2013.","DOI":"10.1109\/CDC.2013.6760020"},{"key":"2026033014320076200_ref057","volume-title":"A dynamic algorithm for facilitated charging of plug-in electric vehicles","author":"Taheri","year":"2011"},{"key":"2026033014320076200_ref058","doi-asserted-by":"crossref","DOI":"10.1007\/b139000","volume-title":"The Theory and Practice of Revenue Management","author":"Talluri","year":"2004"},{"key":"2026033014320076200_ref059","first-page":"1063","volume-title":"Options for control of reactive power by distributed photovoltaic generators","author":"Turitsyn","year":"2011"},{"issue":"8","key":"2026033014320076200_ref060","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1145\/79173.79181","article-title":"A bridging model for parallel computation","volume":"33","author":"Valiant","year":"1990","journal-title":"Communications of the ACM"},{"key":"2026033014320076200_ref061","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1109\/TCST.2009.2017934","article-title":"Fast model predictive control using online optimization","volume":"18","author":"Wang","year":"2010","journal-title":"IEEE Transactions on Control Systems Technology"},{"key":"2026033014320076200_ref062","doi-asserted-by":"crossref","DOI":"10.1002\/9780470466971","volume-title":"Optimization of Power System Operation","author":"Zhu","year":"2009"}],"container-title":["Foundations and Trends\u00ae in Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/ftopt\/article-pdf\/1\/2\/73\/10975812\/2400000002en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ftopt\/article-pdf\/1\/2\/73\/10975812\/2400000002en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T18:32:36Z","timestamp":1774895556000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ftopt\/article\/1\/2\/73\/1324788\/Dynamic-Network-Energy-Management-via-Proximal"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,1]]},"references-count":62,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,1,1]]}},"URL":"https:\/\/doi.org\/10.1561\/2400000002","relation":{},"ISSN":["2167-3888","2167-3918"],"issn-type":[{"value":"2167-3888","type":"print"},{"value":"2167-3918","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,1]]}}}