{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T23:08:13Z","timestamp":1760828893976,"version":"3.37.3"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Swiss Innovation Promotion Agency","award":["10808.1 PFIW-IW"],"award-info":[{"award-number":["10808.1 PFIW-IW"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>The numerical solution of optimal control problems by direct collocation is a widely used approach. Quasi-Newton approximations of the Hessian of the Lagrangian of the resulting nonlinear program are also common practice. We illustrate that the transcribed problem is separable with respect to the primal variables and propose the application of dense quasi-Newton updates to the small diagonal blocks of the Hessian. This approach resolves memory limitations, preserves the correct sparsity pattern, and generates more accurate curvature information. The effectiveness of this improvement when applied to engineering problems is demonstrated. As an example, the fuel-optimal and emission-constrained control of a turbocharged diesel engine is considered. First results indicate a significantly faster convergence of the nonlinear program solver when the method proposed is used instead of the standard quasi-Newton approximation.<\/jats:p>","DOI":"10.1155\/2014\/341716","type":"journal-article","created":{"date-parts":[[2014,3,26]],"date-time":"2014-03-26T03:14:45Z","timestamp":1395803685000},"page":"1-6","source":"Crossref","is-referenced-by-count":1,"title":["Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6141-1450","authenticated-orcid":true,"given":"Jonas","family":"Asprion","sequence":"first","affiliation":[{"name":"Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3204-3446","authenticated-orcid":true,"given":"Oscar","family":"Chinellato","sequence":"additional","affiliation":[{"name":"FPT Motorenforschung AG, Schlossgasse 2, 9320 Arbon, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8781-3199","authenticated-orcid":true,"given":"Lino","family":"Guzzella","sequence":"additional","affiliation":[{"name":"Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland"}]}],"member":"311","reference":[{"volume-title":"On the unconstrained optimization of partially separable functions","year":"1981","key":"1"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01407874"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01589116"},{"first-page":"311","volume-title":"Large scale unconstrained optimization","year":"1996","key":"4"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0098-1354(84)87012-X"},{"issue":"4","key":"6","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/0098-1354(94)00064-U","volume":"19","year":"1995","journal-title":"Computers and Chemical Engineering"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.2514\/3.21662"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.2514\/1.20478"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-007-9098-9"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.06.048"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144502417715"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718577"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.2514\/1.A32071"},{"year":"2006","series-title":"Springer Series in Operations Research and Financial Engineering","key":"14"},{"key":"25","series-title":"The IMA Volumes in Mathematics and its Applications","first-page":"301","volume-title":"Sequential quadratic programming methods","volume":"154","year":"2012"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2013.05.039"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/286538"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0559-y"},{"year":"2006","series-title":"Scientific Computation","key":"22"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(99)00134-X"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1002\/0470868279"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/341716.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/341716.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/341716.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T06:21:40Z","timestamp":1498112500000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/341716\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":21,"alternative-id":["341716","341716"],"URL":"https:\/\/doi.org\/10.1155\/2014\/341716","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}